line segment joining the midpoints of two parallel chords of a circle passes through the centre. AB and CD are two equal chords of a circle with centre O. If AB and CD, on being produced meet at a point P outside the circle, prove that:-

Question

(i) PA=PC (ii) PB=PD

Answer 1

draw PQ through O. It passes through the midpoints of AC and BD.
PQ bisects angle P.
Congruent triangles can prove the statements above.