Question

In the figure, if $OA=17cm$, $AB=30cm$ and OD is perpendicular to AB, then CD is equal to :

• A. 8cm
• B. 9cm
• C. 10cm
• D. 11cm

Answer 1

The correct option is B 9cm

OA and OD are the radii of the circle

by Pythagoras theorem in right triangle OCA

${AO}^2={OC}^2+{AC}^2$

$OC=\sqrt{{OA}^2-{AC}^2}$

$OC=\sqrt{{17}^2-{15}^2}$ [perpendicular drawn from cenentre bisect the chord]

$OC=8cm$

$CD=OD-OC$

$CD=17cm-8cm$

$CD=9cm$

So, option B is the answer.