construction of tangents to a circle

Question

DRAW THE TWO TANGENTS FROM A POINT WHICH IS 10CM AWAY FROM THE CENTRE OF A CIRCLE OF RADIUS 6CM.ALSO, MEASURE THE LENGTHS OF THE TANGENTS

Answer 1

A tangent at a point forms a right angle with the radius. The outside point 10 cm from the centre of the circle is the hypotenuse of two conjoined right triangles. One leg has length 6cm, being the radius of the circle, so the other leg has length √(10²-6²)=√(100-36)=√64=8cm.

Each tangent has length 8cm.