Q. 25

In the given figure, O is the center of the circle. AB is the tangent to the circle at the point P. If APQ = 58° then the measure of PQB is


A. 32°

B. 58°

C. 122°

D. 132°

Answer :


In the given Figure, Join OP


Now, OP AB


[Tangents drawn at a point on circle is perpendicular to the radius through point of contact]


∴∠OPA = 90°


OPQ + APQ = 90°


OPQ + 58° = 90°


[Given, APQ = 58°]


OPQ = 32°


In OPQ


OP = OQ


[Radii of same circle]


OQP = OPQ


[Angles opposite to equal sides are equal]


PQB = 32°


[As OQP = PQB ]

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