Question

PQ and RS are two chords of a circle with centre O. The perpendiculars drawn from O to PQ and RS are OX and OY respectively. Show that PQ² - RS² = 4OY - 4OX.​

Answer 1

Explanation:

Radii PO and RO will be called r

Pythagorean theorem

r² = PX² + OX²

r² = RY² + OY²

PX² + OX² = RY² + OY²

PX² - RY² = OY² - OX²

similar triangles based on diameters rather than radii

(2PX)² - (2RY)² = (2OY)² - (2OX)²

PQ² - RS² = 4OY² - 4OX²

Going by the picture provided rather than your posted question which is missing a couple of squaring exponents on the right hand terms.