Question

If the length of a chard, or a circle is 16 cm, and
lis at a distance of 15 cm, from the centre
of the circle then the radius of a Circle?​

Answer 1

A half of the chord PQ, the radius OM that bisects the chord PQ at A and radius OQ, form a right triangle AOQ that has OA=15cm and OQ=8cm and the third side AQ is to be found.

Here, we can use the Pythagoras Theorem as follows:

${AQ}^{2} = {OA}^{2} + {OQ}^{2} \\ {AQ}^{2} = {15}^{2} + {8}^{2} \\ {AQ}^{2} = 225 + 64 \\ {AQ}^{2} = 289 \\ AQ = 17cm$

Hope this helps.

Hope this helps. Thanks.

Answer 2

$\sf{\huge{\underline{\green{Given :-}}}}$

• The length of a chord of a circle is 16 cm.

• It lies at a distance of 15 cm, from the centre of the circle.

$\sf{\huge{\underline{\green{To\:Find :-}}}}$

• The radius of a circle .

$\sf{\huge{\underline{\green{Answer :-}}}}$

According to the question,

A chord is of length 16 cm is drawn on a circle.

It lies at a distance of 15 cm, from the centre of the circle.

It makes a fig. as per i drawn in attachment.

Join O to A, such that OA is radius of the circle.

It forms a perpendicular OC on Chord AB.

AB = AC + BC

AC = BC

➝ AB = AC + AC

➝ AB = 2AC

➝ 16 = 2AC

➝ AC = 16/2

➝ AC = 8 cm

• AC = 8 cm

• OC = 15 cm

• OA = ??

In right Δ ABC,

OA² = OC² + AC²

➝ OA² = 15² + 8²

➝ OA² = 15² + 64

➝ OA² = 225 + 64

➝ OA² = 289

➝ OA = √289

➝ OA = 17 cm

The radius of a circle is 17 cm.