(Q6) How can you prove the converse of the above theorem.

If a line in the plane of a circle is perpendicular to the radius at its end point on the circle, then the line is tangent to the circle.

Given : Circle with center 'O' a point A on the circle and the line AT perpendicular to OA

R.T.P :AT is a tangent to the circle at A.

Construction:

OPAT

Suppose is not a tangent then AT produced either way if necessary, will meet the circle again.Let it do so at P, join .

Proof: Since = OP (radii)

∠OAP = ∠ But ∠ OPA = °

Two angles of a triangle are right angles which is impossible

Our supposition is

Hence is a tangent