Circle Tangents Property
Tangents drawn from an external point to a circle are equal in length. In this case, SA and SB are tangents from point S.
Given SA = 12 cm, therefore SB must also be 12 cm.
So, SA = SB = 12 cm.
Analyzing Triangle ASB
Consider the triangle formed by the external point S and the points of tangency A and B, which is triangle ASB.
We know that SA = SB, making triangle ASB an isosceles triangle.
We are given that the angle between the tangents, angle ASB, is 60°.
Determining Chord Length AB
An isosceles triangle with the angle between the equal sides being 60° is always an equilateral triangle.
In an equilateral triangle, all sides are equal in length.
Therefore, the length of the chord AB is equal to the lengths of the tangents SA and SB.
AB = SA = SB
AB = 12 cm
Similar Questions
- 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:
- 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?
- A chord of length 24 cm is at a distance of 5 cm from the centre of a circle. The radius of the circle is ______ cm.
- The sides AB, BC, CD and DA of a quadrilateral ABCD touch a circle at P, Q, R and S, respectively. If AB = 16 cm, DS = 10 cm and RC = 3 cm, then find the perimeter of the quadrilateral ABCD (in cm).
- ABCD is a cyclic quadrilateral whose side AB is a diameter of the circle through A, B, C and D. If $\angle ADC = 129^\circ$, then what is the measure of $\angle BAC$?
- Two equal circles, each having a radius of $24\text{ cm}$, intersect each other, such that each passes through the centre of the other. The length of the common chord is ________ $\text{cm}$.
In the given figure, DE is tangent to the circle at a point B. $\Delta \text{ABC}$ is constructed such that A and C are points on the circumference of the given circle, with $\text{AB} = \text{AC}$. If $\angle \text{ABD} = 65^\circ$, then what is $\angle \text{BAC}$? (Figure is not to scale)
In the given circle, diameter AB is extended to meet chord CD extended at P. If the lengths of the line segments AP, CP and DP are 12 cm, 8 cm and 6 cm, respectively, what is the length of the radius of the circle?
- A point P is 13 cm from the center of a circle. The length of the tangent drawn from P to the circle is 12 cm. Find the radius of the circle.
- AB and CD are two chords of a circle. AB = 6 cm, CD = 8 cm and AB || CD. If the distance between AB and CD is 7 cm and the centre of the circle lies in the interior of the quadrilateral ABCD, then find the radius of the circle (in cm).
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:
- 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?
- A chord of length 24 cm is at a distance of 5 cm from the centre of a circle. The radius of the circle is ______ cm.
