In Figure, PQ and RS are two parallel tangents to a circle with centre O

• Geometry (C10)

In Figure, PQ and RS are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting PQ at A and RS at B. Prove that ∠AOB = 90º.

Answer

∆AOD ≅ AOC (SAS)

⇒ ∠1 = ∠2

Similarly, ∠4 = ∠3

⇒ ∠1 + ∠4 = ∠2 + ∠3 = ½(180º)

⇒ ∠2 + ∠3 = 90°

∠AOB = 90°