Two chords AB and CD intersect at P inside the circle. Prove that the sum of the angles subtended by the arcs AC and BD at the centre O is equal to twice the angle APC.
Given : two chords AB and CD intersect each other at P inside the circle. OA, OB, OC and OD are joined. To prove: ∠AOC + ∠BOD = 2∠APC Construction: Join AD. Proof: Arc AC subtends ∠AOCat the centre and ∠ADCat the remaining Part of the circle. ∠AOC = 2∠ADC …………(1)
Solution Two Chords Ab and Cd Intersect at P Inside the Circle. Prove that the Sum of the Angles Subtended by the Arcs Ac and Bd at the Centre O is Equal to Twice the Angle Apc. Concept: Arc and Chord Properties - If Two Arcs Subtend Equal Angles at the Center, They Are Equal, and Its Converse.