In the given figure, O is the point of intersection of two chords AB and CD such that OB = OD and ∠AOC = 45°. Then, ∠OAC and ΔODB are

Question

In the given figure, O is the point of intersection of two chords AB and CD such that OB = OD and ∠ AOC = 45°. Then, ∠ OAC and ΔODB are

Philoid · Accepted Answer

In Δ DOB and Δ AOC,
∠DOB = ∠AOC = 45° (vertically opposite angle)
∠OAC = ∠ODB (angles in the same segment)

∠OCA = ∠OBD (angles in the same segment)
Therefore, Δ DOB Δ AOC by AA similarity,

Therefore, OC = OA.