. If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords

Construction: Draw OL and OM perpendiculars to chords AB and CD respectively. Join OP. To prove: LOPL = LOPM Proof: Consider triangles OLP and OMP, OL = OM [Equal chords AB and CD are equidistant from the centre of the circle] A(;) C B OP is common. LOLP = LOMP AOLP ::AOMP [RIIS] LOPL = LOPM . [CPCT]