Q. 18 B3.7( 3 Votes )

# Centre of the circle is O and AP, and AQ is tangent of the circle. If ∠OPQ=20°, then what is the value of ∠PAQ?

OPQ = 20° …given

Radius OP is perpendicular to tangent PA at point of contact A

APO = 90°

From figure APO = APQ + OPQ

90° = APQ + 20°

APQ = 70° …(a)

Consider ΔAPQ

AP and AQ are tangents to circle from A

Tangents from a point to a circle are equal

AP = AQ
hence ΔAPQ is a isosceles triangle

APQ = AQP

Using (a)

AQP = 70°

Now

APQ + AQP + PAQ = 180° …sum of angles of triangle

70° + 70° + PAQ = 180°

140° + PAQ = 180°

PAQ = 40°

Hence PAQ is 40°

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