Question -
Answer -
Here chords AB and CDintersect each other at O.
Consider ΔAOB andΔCOD,
∠AOB = ∠COD (They are vertically opposite angles)
OB = OD (Given in thequestion)
OA = OC (Given in thequestion)
So, by SAS congruency,ΔAOB ≅ ΔCOD
Also, AB = CD (ByCPCT)
Similarly, ΔAOD ≅ ΔCOB
Or, AD = CB (By CPCT)
In quadrilateral ACBD,opposite sides are equal.
So, ACBD is aparallelogram.
We know that oppositeangles of a parallelogram are equal.
So, ∠A = ∠C
Also, as ABCD is acyclic quadrilateral,
∠A+∠C = 180°
⇒∠A+∠A = 180°
Or, ∠A = 90°
As ACBD is aparallelogram and one of its interior angles is 90°, so, it is a rectangle.
∠A is the angle subtended bychord BD. And as ∠A = 90°, therefore, BDshould be the diameter of the circle. Similarly, AC is the diameter of thecircle.