Question

The radius of a circle is $13$ cm and the length of one of its chords is $10$ cm. The distance of the chord from the centre is

• A. $8$ cm
• B. $10$ cm
• C. $12$ cm
• D. $6$ cm

Answer 1

Answer: (C)

$12$ cm

Let $AB$ is chord of the circle and $OM\perp AB$

$OA=13$ cm, $AB=10cm$

$\therefore AM=5cm$

In $\Delta AOM$, we have

$(OM{)}^2=(13{)}^2-(5{)}^2$

$=169-25=144c{m}^2$

$\therefore OM=12cm$