SSC CHSL 2020 PYQ — Question 63

Let PQ and PR be the two tangents drawn to the circle of Centre O.

Draw a line segment, from Centre O to external point P.

We know that the tangents make a right angle with a radius of the circle. 

Here, OR and OQ is the radius of the circle

So, ∠OQP = ∠ORP = 90°
Now, it is clear that both the triangles ∆POQ and ∆POR are right-angled triangles and a common hypotenuse OP in them. 

∠PQO = ∠PRO = 90° 
Common hypotenuse OP between them. 

And OQ = OR [Radius of circle]. 
So, by the R.H.S. rule of similarity 

∆POQ ~ ∆POR 

Hence, both the triangles are similar to each other. 

Therefore, 
OP/OP= PQ/PR = OQ/OR 

PQ/PR = 1 

PQ = PR