Question

A chord of a circle of length 12 cm is at the distance of 14 cm from the center of a circle.find the radius of the circle.

Answer 1

$\bold{given : }$

• Length ( 0L ) = 12 cm

• Distance of the chord from the centre( AB )= 14 cm

$\bold{to \: find \: out : }$

Find the radius of the circle ( OA ).

$\bold{Solution: }$

The perpendicular from the centre of a circle to a chord bisects the chord.

Therefore,

AL = LB = ½ AB = ½× 14 = 7 cm

In right triangle OLA , we have

OA² = OL² + AL²

OA² = ( 12 )² + ( 7 )²

OA² = 144 + 49

OA² = 193

OA = √193

OA = 13.89 ( approx )

Hence, the radius of the circle is 13.89 cm.