Question

If a point P is 17 cm from the centre of a circle of radius 8 cm, then find the length of the tangent drawn to the circle from point P.

Answer 1

Let `O` is the center of the circle and tangent touches the circle at point `T`.
Then, triangle OPT will be a right angle triangle.
We are given,
`OP = 17cm, OT = `radius = ` 8cm`
So, `PT^2 = OP^2-OT^2`
`PT^2 = 17^2-8^2 = 289-64 = 225`
`PT = sqrt225 = 15cm`
So, length of tangent will be `15` cm.