A circle with radius r has a tangent line at a point P on the circle. The distance of the tangent from point P to the external point Q is 10 cm. The distance from the center of the circle to point Q is 13 cm. Find the radius of the circle.
√69
The radius drawn to the point of tangency is perpendicular to the tangent line, so triangle OPQ is right-angled at P. By the Pythagorean theorem, \(OQ^2 = OP^2 + PQ^2\), giving \(13^2 = r^2 + 10^2\), so \(r^2 = 169 - 100 = 69\), and \(r = \sqrt{69}\).
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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?
