Question

If AB and CD are two chords of a circle intersecting at point E, as per the given figure, then,​

Answer 1

Answer:

O is centre of circle and arc is AC ∠AOC is angle subtended by arc AC at center, is double the angle ∠ABC, angle at remaining part by same arc ∴ ∠AOC = 2∠ABC Similarly ∠BOD, angle subtended by are BD at center of circle is double the angle at remaining part. ∠BOD = 2∠BCD …..(ii) Adding equation (i) and (ii) ∠AOC + ∠BOD = 2(∠ABC + ∠BCD) ⇒ ∠AOC + ∠BOD = 2∠AEC ⇒ ∠AEC = 1212 [∠AOC + ∠BOD] ⇒ ∠AEC = 1212 [Angle formed at center by CXA angle formed of center by chord DYB]