Question

In the given figure , PA and PB are tangents of a circle with centre O. If the radius of the circle is r ,

then OP $\times$ OQ = _____.

• A. $2r^2$
• B. $\frac{r^2}{2}$
• C. $2r$
• D. $r^2$

Answer 1

The correct option is D

$r^2$

i) OA = OB = r ........(radii of circle)

ii) PA = PB ...........(tangents from an external point are equal)

iii) OAPB is a kite.

$\therefore$ OP bisects AB at right angles

iv) $△OQA\sim △OAP$ ...........(AA Similarity)

$\frac{OA}{OP}$ = $\frac{OQ}{OA}$

$O{A}^2$ = OP $\times$ OQ

$\therefore$ OP$\times$OQ = $r^2$