Question

Q1.8
If two tangents are inclined at 60 degree
are drawn a circle of radius 3 cm then
find length of each tangent.
(1 Point)
54cm
116cm​

Answer 1

Explanation:

✬ Tangents = 3√3 cm ✬

Step-by-step explanation:

Given:

Two tangents are inclined at 60°.

Radius of circle is 3 cm.

To Find:

What is the length of each tangent ?

Solution: Let in circle with centre O.

AO = BO = 3 cm (radii)

PA = PB (tangent)

∠APB = 60°

∠PAO = ∠PBO = 90° (tangent makes right angle at the point of contact)

Construction:

Join PO such that its bisects ∠APB.

Now we have

∠APO = ∠BPO = 30°

Let's consider right angled ∆PBO we have

OB = perpendicular

PB = base

Applying tanθ there

⟹ tanθ = P/B

⟹ tan30° = 3/PB

⟹ 1/√3 = 3/PB

⟹ PB = 3√3

Hence, length of each tangents is 3√3 cm.