The radius of a circle is 13 cm and the length of one of its chords is 10 cm. What is the distance of the chord from the centre?
12 cm
The perpendicular drawn from the centre of a circle to a chord bisects the chord.
So half of the chord length = 10/2 = 5 cm.
Let d be the distance of the chord from the centre. Using the Pythagorean theorem in the right triangle formed by the radius, half-chord and the perpendicular distance: d^2 + 5^2 = 13^2.
d^2 = 169 - 25 = 144, so d = 12 cm.
Important Questions from Circles, Chords and Tangents
In a circle, a ten cm long chord is at a distance of 12 cm from the centre of the circle. The length of the diameter of the circle (in cm) is:
Chord AB of a circle of radius 10 cm is at a distance 8 cm from the centre O. If tangents drawn at A and B intersect at P., then the length of the tangent AP (in cm) is:
A chord 21 cm long is drawn in a circle of diameter 25 cm. The perpendicular distance of the chord from the centre is:
In a circle with radius 5 cm, a chord is at a distance of 3 cm from the centre. The length of the chord is:
O is the centre of this circle. Tangent drawn from a point P, touches the circle at Q. If PQ = 24 cm and OQ = 10 cm, then what is the value of OP?
