Question

A chord XY of a circle with centre O is bisected at M by its diameter RS.The radius OS and OR is 15 cm, OM is 9 cm. Find the length of the chord RY.

• A. $12\sqrt{5}$ cm .
• B. 12 cm
• C. $11\sqrt{5}$ cm .
• D. 11 cm

Answer 1

The correct option is A

$12\sqrt{5}$ cm .

Radius OX = 15 cm, OM = 9 cm (given)

$\therefore$ in right angled triangle OXM

$X{M}^2=O{X}^2-O{M}^2$

= ${15}^2-9^2$

= 225 - 81 = 144

XM = $\sqrt{144}$ = 12 cm.

$\therefore$ XM =MY = 12 cm

RM = RO + OM

= 15 + 9

= 24 cm

In right angled triangle RMY

$R{Y}^2=R{M}^2-M{Y}^2$

= ${24}^2+{12}^2$

= 576 + 144 = 720

RY = $\sqrt{720}$ = $12\sqrt{5}$ cm .