Question

in the figure ABCD is a cyclic quadrilateral the tangents at the points A and C of meet each other at the point P if angle abc =100 then find measure of angle APC.​

Answer 1

∠APC = 20° if in the figure ABCD is a cyclic quadrilateral the tangents at the points A and C of meet each other at the point P & ∠ABC = 100°

Step-by-step explanation:

ABCD is a cyclic quadrilateral

=> ∠ABC + ∠ADC = 180°

=> 100° + ∠ADC = 180°

=> ∠ADC = 80°

∠AOC = 2 ∠ADC  ( angles subtended by arc AC at center )

=> ∠AOC = 2 * 80°

=> ∠AOC = 160°

in Quadrilateral AOCP

∠OAP + ∠AOC + ∠OCP + ∠APC = 360°

∠OAP  = ∠OCP =  90°  ( Tangents)

=> 90° + 160° + 90° + ∠APC = 360°

=> ∠APC = 20°

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