Question

The radius of a circle is 8 cm. Calculate the length of a tangent drawn to this circle from a point at a distance of 10 cm from its centre.

• A. 9 cm
• B. 7 cm
• C. 2 cm
• D. 6 cm

Answer 1

The correct option is D

6 cm

Given: OP = 10 cm and radius OT = 8 cm

$\because OT\perp PT$ [By Theorem- The tangent at any point of a circle is perpendicular to the radius through the point of contact.]

$\therefore$ Applying pythagoras theorem in right $\Delta OTP$,

$O{P}^2=O{T}^2+P{T}^2\Rightarrow (10{)}^2=(8{)}^2+P{T}^2$

$\Rightarrow 100=64+P{T}^2\Rightarrow P{T}^2=100-64=36$

$\therefore PT=\sqrt{36}=6cm$