Question

Two chords PQ and RS intersect at point O inside the circle. If OP = 4 cm, OQ = 9 cm and RS = 12 cm, then find the length of OR.

Answer 1

When two chords intersect each other within a circle, the product of the chord segments will be equal.
So, $OP\times OQ=OR\times OS$
Let the value of OR be 'x' cm
4 $\times$ 9 = x $\times$ (12 - x)(1 mark)
$36=12x-x^2$
$x^2-12x+36=0$
$(x-6{)}^2=0$
x = 6 cm (2 marks)

Hence, the length of OR is 6 cm.