Theorem 1 The first theorem about a cyclic quadrilateral state that: The opposite angles in a cyclic quadrilateral are supplementary. i.e., the sum of the opposite angles is equal to 180˚. Consider the diagram below. If a, b, c, and d are the inscribed quadrilateral’s internal angles, then a + b = 180˚ and c + d = 180˚. Let’s prove that;

All I can find are videos proving that the measure of an inscribed angle is half the measure of a central angle that subtends the same arc, which seems related to, but not quite the same as what he is getting at here. Could anyone point me in the direction of the video/ explain the connection between these two ideas? • 3 comments ( 27 votes) Upvote

Apparently there is a nice theorem related to the anticenter of a cyclic quadrilateral that is not mentioned in the wikipedia: Anticenter of the cyclic quadrilateral, the intersection point of its diagonals and two intersection points of the lines that contain its opposite sides are always concyclic.

ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 140º, then ∠BAC is equal to: (A) 80º (B) 50º (C) 40º (D) 30º #Exemplar Maths for Class 9 #Circles #Maths #NCERT #1.3 #9.1 #10.1 #10.2 #10.3 #10.4 1.0 1.0 1.0 1.0 2.0 2.0 2.0 2.0 3.0 3.0 3.0 3.0 4.0 4.0 4.0 4.0 5.0 5.0 5.0 5.0 6.0 6.0 6.0 6.0

The body is a complex organism, and as such, it takes energy to maintain proper functioning. Adenosine triphosphate (ATP) is the source of energy for use and storage at the cellular level. The structure of ATP is a nucleoside triphosphate, consisting of a nitrogenous base (adenine), a ribose sugar, and three serially bonded phosphate groups. ATP is commonly referred to as the "energy currency.