State True or False.

Construction of a pair of tangents to a circle of radius 3 cm which are inclined to each other at an angle of 60 $0$ is represented by the following figure.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

True

False

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

We know that tangent is perpendicular to the radius at the point of contact.
∴ ∠A = ∠C = 90⁰
Already given tangents are inclined at an angle 60⁰.
∴ ∠C = 60⁰
We know that the sum of angles of a quadrilateral is 360⁰.
For quadrilateral AOCP,
∠A + ∠O + ∠C + ∠P = 360⁰
∠O + 90⁰ + 60⁰ + 90⁰ = 360⁰
∠O + 240⁰ = 360⁰
∠O = 120⁰.
Draw a circle of radius of 3 cm with center O.
Now, draw radius OA and draw an angle of 120⁰ from radius.
∠AOC = 120°.
Draw perpendiculars AM and CN from points A and C.
Extend the perpendiculars to intersect each other at point P.
Then, PA and PC are the required tangents to the given circle inclined to each other at an angle of 60°.
Hence, the required tangents to the given circle of radius 3cm inclined to each other at an angle of 60° are,
solution

Therefore, the given figure is true.
The correct option is (1).

Watch 3-min video & get full concept clarity