Question

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Answer 1

$\huge{\mathfrak{\underline{\underline{\red{Question:-}}}}}$

Find the length of PR in the adjoining figure, if O is the centre of the circle of radius 5cm and OP = 13cm.

$\huge{\mathfrak{\underline{\underline{\pink{Solution:-}}}}}$

First of all, join OR.

Now,

OQ | PQ ( Transversal at any point of the circle is prependicular to the radius of circle through point of contact )

Therefore, angle OQP = 90°

Now, in Triangle OQP

By Pythagoras theorem

(OP)² = (OQ)²+(QP)²

= (5)²+(13)²

= 25 + 169

(OP)² = 194

OP = √194cm

Since OP is radius and OR is also radius, therefore

OP = OR

In triangle ORP

by Pythagoras theorem

(OP)² = (OR)²+(RP)²

(√194)² = (5)²+ (RP)²

194 = 25 + (RP)²

169 = (RP)²

RP = √169cm

$\huge{\boxed{RP = 13cm}}$