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 isA. 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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