Question

From a point P, 10 cm away from the centre of a circle, a tangent PT of length 8 cm is drawn. Find the radius of the circle.

Answer 1

Let O be the centre of the given circle and let P be a point such that OP = 10 cm.

Let PT be the tangent such that PT = 8 cm.

Join OT.

Now, PT is a tangent at T and OT is the radius through T.

Therefore, $OT\perp PT$.

Using pythagoras theorem in $△OTP$, we have,

$O{P}^2=O{T}^2+P{T}^2$

$O{T}^2=100-64=36$

$OT=6cm$

Therefore, the radius of the circle is 6 cm.