A tangent is drawn to a circle of radius 12 cm from a point situated at a distance of 13 cm from the centre of the circle. The length of the tangent will be:
5 cm
A tangent to a circle is perpendicular to the radius at the point of contact, so the radius, the tangent, and the line joining the external point to the centre form a right triangle.
Here the hypotenuse is the distance from the external point to the centre (13 cm) and one leg is the radius (12 cm); the other leg is the required tangent length \(t\).
By Pythagoras: \(t^2 = 13^2 - 12^2 = 169 - 144 = 25\), so \(t = 5\) cm.
Hence, the length of the tangent is 5 cm.
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Important Questions from Circles, Chords and Tangents
- A circular coin of radius 1 cm is allowed to roll freely on the periphery over a circular disc of radius 10 cm. If the disc has no movement and the coin completes one revolution rolling on the periphery over the disc and without slipping, then what is the number of times the coin rotated about its centre ?
There are two concentric circles. The radii of the two circles are 100 m and 110 m respectively. A wheel of radius 30 cm rolls on the smaller circle and another wheel rolls on the larger circle. After they have completed one revolution, it is found that the two wheels rolled equal number of times
on their respective axes. What is the radius of the other wheel ?- The length of a tangent drawn to a circle of radius 4 cm from a point 5 cm away from the center of the circle is:
- If SA and SB are tangents to a circle from an outside point S, such that SA = 12 cm and angle ASB = 60°. What will the length of chord AB be?
- In a circle, two chords of lengths x and y subtend the angles of $60^{\circ}$ and $90^{\circ}$ at the center respectively. Which of the following is correct in this scenario?
