Question

In the figure at right, AB and CD are two parallel chords of a circle with centre O and radius $$5 cm. Such that AB = $8$ cm and CD = $6$ cm. If $OP\perp AB$ and $OQ\perp CD$ determine the length PQ.

Answer 1

Given $OP\perp AB$ and $OQ\perp CD$

CQ = QD = $3$ cm

AP = BP = $4$cm

In $△OPA$

$O{P}^2=O{A}^2–A{P}^2=r^2–4^2=25–16=9$

$⟹OP=3$

In $△OCQ$

$O{Q}^2=\sqrt{r^2–3^2}=4$

$PQ=OP+OQ=4+3=7cm$