Question

in a circle, the perpendicular form the centre to a chord bisect the chord.

Answer 1

by RHS congruency
by CPCT
PR=RQ

Answer 2

In the diagramAB is the chord of a circle with centre O.

OM is the perpendicular from the centre to the chord.

triiangles OAM and OBM.

The hypotenuses (OA and OB) are the same, as they are both the radius of the circle.

OM is common to both triangles.

OMA and OMB are both right angles.

Triangles OAM and OBM are congruent (RHS), so it follows that AM = MB.

Therefore, M is the midpoint of AB, and the chord has been bisected.