A circular park of radius 20m is situated in a colony. three boys ankur, syed and david are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. find the length of the string of each phone.

Given below are the Class 9 Maths Assignments for Circles a) Concepts questions b) Calculation problems c) Multiple choice questions d) Long answer questions e) Fill in the blank's Q1. If two intersecting chords of a circle make equal angles with the diameter passing through their point of intersection, prove that the chords are equal. Q2. If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angle with the chords. Q3. If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D. Prove that AB = CD. Q4. Three girls Reshma, Salma and Mandip are playing a game by standing a circle of radius 5m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If the distance between Salma and Mandip is 6 m each, what is the distance between Reshma and Mandip. Q5. A circular park of radius 20m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. Find the length of the string of each phone. Q6. Prove that the quadrilateral formed (if possible) by the internal angle bisectors of any quadrilateral is cyclic. Q7. If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that is a rectangle. Q8. If the non- parallel sides of a trapezium are equal. Prove that its equal ...

It is given that AS = SD = DA Therefore, Δ A S D is an equilateral triangle. The radius, OA = 20 m The medians of the equilateral triangle pass through the circumcentre (O) of the equilateral triangle ASD. We also know that medians intersect each other in the ratio 2:1. Let AB be the median of the equilateral triangle ASD, so we can write ⇒ O A O B = 2 1 ⇒ 20 m O B = 2 1 ⇒ O B = ( 20 2 ) m = 10 m ∴ A B = O A + O B = ( 20 + 10 ) m = 30 m In Δ A B D, A D 2 = A B 2 + B D 2[using pythagoras theorem] A D 2 = ( 30 ) 2 + ( D S 2 ) 2 We have AS = SD = DA, ∴ A D 2 = ( 30 ) 2 + ( A D 2 ) 2 A D 2 = 900 + 1 4 A D 2 3 4 A D 2 = 900 A D 2 = 1200 A D = 20 √ 3 Therefore, the length of the string of each phone will be 20 √ 3 m.

Views: 5,709 × ° Surface areas a … khanacademy.org Volume of cylinders, spheres, and ... After painting his porch, Jamil has 4 1 ​ of a can of paint remaining. The can has a radius of 8 cm and a height of 20 cm. He wants to pour the remaining paint into a smaller can for storage. The smaller can has a radius of 5 cm. What does the height of the smaller can need to be to hold all of the paint? Stuck? Review related articles/videos or use a hint. Check again A circular park of radius 20m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. Find the length of string of each phone Updated On Feb 19, 2023 Topic All topics Subject Mathematics Class Class 9 Answer Type Video solution: 1 Upvotes 82 Avg. Video Duration 11 min

It is given that AS = SD = DA Therefore, ΔASD is an equilateral triangle. OA (radius) = 20 m Medians of equilateral triangle pass through the circum centre (O) of the equilateral triangle ASD. We also know that medians intersect each other in the ratio 2: 1. As AB is the median of equilateral triangle ASD, we can write `rArr(OA)/(OB) = 2/1` `rArr(20m)/(OB) = 2/1` `rArrOB=(20/2)m = 10m` ∴ AB = OA + OB = (20 + 10) m = 30 m In ΔABD, AD 2= AB 2+ BD 2 AD 2= (30) 2+ (AD/2) 2 `AD^2= 900 + 1/4AD^2` `3/4AD^2 = 900` `AD^2 = 1200` `AD = 20sqrt3` Therefore, the length of the string of each phone will be`20sqrt3" m"`

A circular park of radius 20m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. Find the length of string of each phone Solution: Centre and Centroid are the same for an equilateral triangle, and it divides the median in the ratio 2 : 1. Let A, D, S denote the positions of Ankur, David, and Syed, respectively. ∆ADS is an Let B denote the mid-point of DS, and hence AB is the median and perpendicular bisector of DS. Hence ∆ABS is a right-angled triangle with ∠ABS = 90º. O (centroid) divides the line AB in the ratio 2 : 1. So OA : OB = 2 : 1. OA/OB = 2/1 Since OA = 20 (given) thus, OB = 10m AB = OA + OB = 20 + 10 = 30 m ….(1) Let the side of the equilateral triangle ∆ADS be 2x. AD = DS = SA = 2x …. (2) Since B is the mid-point of DS, we get BS = BD = x …. (3) Applying Pythagoras theorem to ∆ABD, we get: AD 2 = AB 2 + BD 2 (2x) 2 = 30 2 + x 2 4x 2 = 900 + x 2 3x 2 = 900 x 2 = 300 x = 10√3 x = 17.32 AD = DS = SA = 2x = 34.64 m Length of the string = Distance between them = AD or DS or SA = 34.64 m. ☛ Check: Video Solution: A circular park of radius 20m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk to each other. Find the length of string of each phone Summary: If a circular park of radius of 20m is situated in a colony, three boys Ankur, Syed, and David are si...

More • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • CBSE Study Material • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • NCERT Solutions for Class 9 Maths Exercise 10.4 Chapter 10 Circles * According to the CBSE Syllabus 2023-24, this chapter has been renumbered as Chapter 9. NCERT Solutions for Class 9 Maths Chapter 10 – Circles Exercise 10.4 is available here in PDF format, which st...

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• Course • NCERT • Class 12 • Class 11 • Class 10 • Class 9 • Class 8 • Class 7 • Class 6 • IIT JEE • Exam • JEE MAINS • JEE ADVANCED • X BOARDS • XII BOARDS • NEET • Neet Previous Year (Year Wise) • Physics Previous Year • Chemistry Previous Year • Biology Previous Year • Neet All Sample Papers • Sample Papers Biology • Sample Papers Physics • Sample Papers Chemistry • Download PDF's • Class 12 • Class 11 • Class 10 • Class 9 • Class 8 • Class 7 • Class 6 • Exam Corner • Online Class • Quiz • Ask Doubt on Whatsapp • Search Doubtnut • English Dictionary • Toppers Talk • Blog • Download • Get App Solution Let Ankur be represented as A, Syed as S and David as D. The boys are sitting at an equal distance. Hence, △ A S D is an equilateral triangle. Let the radius of the circular park be r meters. O S = r = 20 m . Let the length of each side of △ A S D be x meters. Draw A B ⊥ S D S B = B D = 1 2 S D = x 2 m In △ A B S , ∠ B = 90 ∘ By Pythagoras theorem, A S 2 = A B 2 + B S 2 A B 2 = A S 2 − B S 2 x 2 − ( x 2 ) 2 = 3 x 2 4 A B = √ 3 x 2 m Now, A B = A O + O B O B = A B − A O O B = ( √ 3 x 2 − 20 ) m In △ O B S , O S 2 = O B 2 + S B 2 20 2 = ( √ 3 x 2 − 20 ) 2 + ( x 2 ) 2 400 = 3 4 x 2 + 400 − 2 ( 20 ) √ 3 x 2 ) + x 2 4 0 = x 2 − 20 √ 3 x x = 20 √ 3 m The length of the string of each phone is 20 √ 3 m. Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If t...

• Course • NCERT • Class 12 • Class 11 • Class 10 • Class 9 • Class 8 • Class 7 • Class 6 • IIT JEE • Exam • JEE MAINS • JEE ADVANCED • X BOARDS • XII BOARDS • NEET • Neet Previous Year (Year Wise) • Physics Previous Year • Chemistry Previous Year • Biology Previous Year • Neet All Sample Papers • Sample Papers Biology • Sample Papers Physics • Sample Papers Chemistry • Download PDF's • Class 12 • Class 11 • Class 10 • Class 9 • Class 8 • Class 7 • Class 6 • Exam Corner • Online Class • Quiz • Ask Doubt on Whatsapp • Search Doubtnut • English Dictionary • Toppers Talk • Blog • Download • Get App Solution Let Ankur be represented as A, Syed as S and David as D. The boys are sitting at an equal distance. Hence, △ A S D is an equilateral triangle. Let the radius of the circular park be r meters. O S = r = 20 m . Let the length of each side of △ A S D be x meters. Draw A B ⊥ S D S B = B D = 1 2 S D = x 2 m In △ A B S , ∠ B = 90 ∘ By Pythagoras theorem, A S 2 = A B 2 + B S 2 A B 2 = A S 2 − B S 2 x 2 − ( x 2 ) 2 = 3 x 2 4 A B = √ 3 x 2 m Now, A B = A O + O B O B = A B − A O O B = ( √ 3 x 2 − 20 ) m In △ O B S , O S 2 = O B 2 + S B 2 20 2 = ( √ 3 x 2 − 20 ) 2 + ( x 2 ) 2 400 = 3 4 x 2 + 400 − 2 ( 20 ) √ 3 x 2 ) + x 2 4 0 = x 2 − 20 √ 3 x x = 20 √ 3 m The length of the string of each phone is 20 √ 3 m. Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If t...

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