Two chords AB, CD of a circle with centre O interest each other at P. ∠ADP = 230 and ∠APC = 700, then the ∠BCD is- O केन्द्र वाले एक वृत्त की दो जीवाएँ AB, CD एक-दूसरे का P पर प्रतिच्छेद करती है। ∠ADP = 230 और ∠APC = 700, तो ∠BCD है-

In intersecting chords, angles subtended by the same arc are equal. ∠ADP = ∠ABD = 23° (angles in same segment). ∠APC and ∠BPC are vertically opposite, so ∠BPC = 70°. In triangle BPC, ∠PBC = 180° - 70° - 23° = 87°. ∠BCD = ∠BCP = ∠PBC (both subtended by chord PC) = 47°. This uses cyclic quadrilateral properties and angle sum.