Question

pq is a tangent to a circle with centre o at point p. If triangle opq is an isosceles triangle, then find angle oqp​

Answer 1

Angle OPQ+ Angle PQO+ Angle QOP=180°.......Angle sum property of triangle

Let Angle POQ=x

Lx+Lx+90°=180°

2Lx=180°-90°

Lx=90/2

Lx=45°

Hence, LOPQ=45°.

Hope it helps mate.

Answer 2

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pq is tangent and Oq is radius

we know that tangent is perpendiculatr to radius

Angle Opq = 90°

Angle OPQ is isoceles

OP = PQ

Angle OQP = Angle POQ

SO,

angle Oqp = 1/2 X 90°

= 45°

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