Q48 of 186 Page 263

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

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.

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