Answer the following questions about tangents to a circle with centre O.
(i) State the theorem relating the lengths of the two tangents drawn from an external point to a circle.
(ii) Prove that for any two external points P and Q,
(OP)2−(OQ)2=(PT)2−(QS)2,
where PT and QS are the lengths of the tangents drawn from P and Q respectively.
(iii) Using the result of part (ii), find the length of the tangent drawn from a point Q whose distance from O is 26 cm, given that another point P is 20 cm from O and the length of the tangent from P is 12 cm.