Points A and B are on circle with centre O. PA and PB are tangents to the circle from an external point P. If PA and PB are inclined to each other at 42°, then find the measure of ∠OAB.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 21°
Calculations:
Consider the quadrilateral AOBP in which
∠A + ∠O + ∠B + ∠P = 360 (sum of internal angles of an quadrilateral is 360)
⇒ 90 + ∠O + 90 + 42 = 360
⇒ ∠O = 360 - 90 - 90 - 42 = 138
Triangle OAB is an isosceles triangle as OA = OB (radius of cirlce)
⇒ ∠O + ∠OAB + ∠OBA = 180 (∠OAB = ∠OBA = x)
⇒ 138 + 2x = 180
⇒ 2x = 42
⇒ x = 21
Hence, ∠OAB is 21°