Question

Two circles intersect each other at O and P. AB is a common tangent to the circles. Then the angles subtended by the line segment AB at O and P are:

(a) complementary 

(b) supplementary 

(c) equal 

(d) None of these

Answer 1

Answer : (B) supplementary

∠OAB = ∠OPA 

∠OBA = ∠OPB {Angles in alternate segment are equal.} 

∴ ∠OAB + ∠OBA 

= ∠OPA + ∠OPB = ∠APB. 

In ∆AOB, ∠AOB 

= 180º – (∠OAB + ∠OBA) = 180º – ∠APB 

⇒ ∠AOB + ∠APB = 180º. 

i.e., ∠s AOB and APB are supplementary.