Question

In the figure, PT is a tangent to the circle with centre O. If $PT=30$ cm and diameter of the circle is 32 cm, then the length of line segment OP will be

• A. 68 cm
• B. 34 cm
• C. 17 cm
• D. 34.8 cm

Answer 1

Answer: (B)

34 cm

Given $PT=30cm$

$OT$ is the radius of a cicle

therefore $OT$ will be half of given diameter

$OT$ = $16cm$

$\angle OTP$ = ${90}^{\circ }$ (tangent is perpendicular to radius at point of contact)

now apply pythoguras theorem to

${OP}^2={OT}^2+{TP}^2$

${OP}^2={16}^2+{30}^2$

$OP=\sqrt{1156}$

$OP=34$

So answer will be option B.