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.

Answer 1

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.