Question

If the length of a chord of a circle is 16 cm and is at a distance of 15 cm from the centre of the circle, then the radius of the circle is

• A. 15 cm
• B. 16 cm
• C. 17 cm
• D. 34 cm

Answer 1

The correct option is C

17 cm

Length of chord AB of cirlce = 16 cm

Distance from the centre OL = 15 cm

Let OA be the radius, then in right $\Delta OAL$,

$O{A}^2=O{L}^2+A{L}^2$

$=(15{)}^2+{\left(\frac{16}{2}\right)}^2={15}^2+8^2$

$=225+64=289=(17{)}^2$

$\therefore OA=17cm$

Hence radius of the circle = 17 cm