Advertisements
Advertisements
Question
A tangent JK is drawn to a circle with centre C such that CK = 6 cm and ∠CKJ = 60°. Find the length of the tangent JK.
Solution
JK is a tangent at the point J and CJ is a radius.
So, CK = 6 cm and ∠CKJ = 60° ......[Given]
Now, ∠CKJ = 90° ......[Tangent theorem]
In ΔCJK,
cos 60° = `"Base"/"Hypotenuse"`
⇒ cos 60° = `(JK)/(KC) = (JK)/6`
⇒ `1/2 = (JK)/6`
⇒ JK = 3
Hence, the length of JK is 3 cm.
APPEARS IN
RELATED QUESTIONS
Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
A circle touches all the four sides of a quadrilateral ABCD. Prove that AB + CD = BC + DA.
In the given figure O is the centre of the circle and AB is a tangent at B. If AB = 15 cm and AC = 7.5 cm. Calculate the radius of a circle.
In Figure 3, a right triangle ABC, circumscribes a circle of radius r. If AB and BC are of lengths of 8 cm and 6 cm respectively, find the value of r.
Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8 cm is a tangent to the inner circle. Find the radius of the inner circle.
A chord of a length 16.8 cm is at a distance of 11.2 cm from the centre of a circle . Find the length of the chord of the same circle which is at a distance of 8.4 cm from the centre.
In following fig., PT is a tangent to the circle at T and PAB is a secant to the same circle. If PA = 4cm and AB = Scm, find PT.
In following fig., PT is a tangent to the circle at T and PAB is a secant to the same circle. If PB = 9cm and AB = Scm, find PT.
In followinf fig., two concentric circles with centre 0 are of radii 5 cm and 3 cm. from an external point P, tangents PA and PB are drawn to these circles. If AP = 12cm, find BP.
In the alongside, figure, O is the centre of the circumcircle of triangle XYZ. Tangents at X and Y intersect at T. Given ∠XTY = 80° and ∠XOZ = 140°. Calculate the value of ∠ZXY.
In the given figure, diameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T. CD = 7.8 cm, PD = 5 cm, PB = 4 cm. Find:
- AB.
- the length of tangent PT.
The tangents drawn at the extremities of the diameter of a circle are ______.
Construct a pair of tangents to a circle of radius 4 cm, which are inclined to each other at an angle of 60°.
Construct a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°.
In the given figure, PQ is a tangent to the circle with centre O. If ∠OPQ = x, ∠POQ = y, then x + y is ______.
The length of tangent drawn to a circle of radius 9 cm from a point 41 cm from the centre is ______.
In the given figure, O is the centre of the circle. PQ is a tangent to the circle at T. Chord AB produced meets the tangent at P.
AB = 9 cm, BP = 16 cm, ∠PTB = 50° ∠OBA = 45°
Find:
- Length of PT
- ∠BAT
- ∠BOT
- ∠ABT
In the given figure, AB and AC are tangents to the circle. If ∠ABC = 42°, then the measure of ∠BAC is ______.
In the given diagram, PS and PT are the tangents to the circle. SQ || PT and ∠SPT = 80°. The value of ∠QST is ______.
