Question

P is a point on a circle with centre O. I draw a tangent of the circle at the pont P and cut off a part 'PQ' equal in length to the radius of the circle, from the tangent. I draw another tangent QR of the circle from the point Q and write the value of angle PQR by measuring by a protractor​

Answer 1

Answer:

Given- PQ is a tangent to a circle with centre O at Q. QOR is a diameter of the given circle so that ∠POR=120

o

. To find out- ∠OPQ=?

Solution- QOR is a diameter.

∴OQ is a radius through the point of contact Q of the tangent PQ. ∴∠OQP=90

o

since the radius through the point of contact of a tangent to a circle is perpendicular to the tangent.∴∠OPQ+∠OQP=120

o

(external angles of a triangle=sum of the internal opposite angles )

∴∠OPQ=120

o

−90

o

=30

o

.

Ans- Option C.

solution