Tangent circle Theorem

Theorem 1:- If two chords of a circle intersects internally or externally, then the rectangle formed by the two parts of one chord is equal in area to the rectangle formed by the two parts of the other. Given:- Two chords AB and CD of a circle intersect each other at a point P lying inside in circle (i) outside the circle (ii) of the circle. To prove: - PA.PB = PC.PD Construction:-AC and BD are join P. Proof:- Case - (1) in circle  (i) P lies inside the circle case 2: - (1) in circle  (i) P lies outside the circle