Q. 14.3( 39 Votes )

# A chord of length 16 cm is drawn in a circle of radius 10 cm. Find the distance of the chord from the center of the circle.

Answer :

Let AB be a chord of a circle with center O. OCAB, then

AB = 16 cm, and OA = 10 cm.

OCAB

Therefore,

OC bisects AB at C

AC = (1/2) AB

⇒ AC = (1/2) 16

⇒ AC = 8 cm

In triangle OAC,

OA^{2} = OC^{2} + AC^{2}

⇒ 10^{2} = OC^{2} + 8^{2}

⇒ 100 = OC^{2} + 64

⇒ OC^{2}= 36

⇒ OC= 6

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

RELATED QUESTIONS :

PQ and RQ are the chords of a circle equidistant from the centre. Prove that the diameter passing through Q bisects ∠PQR and ∠PSR.

RS Aggarwal & V Aggarwal - Mathematics