Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Home

In the adjoining figure. If AB is a chord of the circle with c

Question

In the adjoining figure. If $A B$ is a chord of the circle with centre $O, A OC$ is a diameter and $A T$ is the tangent at $A$ . Prove that $∠ B A T = ∠ A CB$

Views: 703 students

Found 2 tutors discussing this question

Scarlett Discussed

In the adjoining figure. If

A B

is a chord of the circle with centre

O, A OC

is a diameter and

A T

is the tangent at

A

. Prove that

∠ B A T = ∠ A CB

5 mins ago

Discuss this question LIVE

5 mins ago

Text solutionVerified

Given:-

A B

is chord.

A OC

is diameter

A T

is a tangent to the circle at

A

To prove:-

∠ B A T = ∠ A CB

Proof:-

∠ O A T = 90^{\circ}

(tangent is perpendicular to the radius )

\Rightarrow ∠ O A B + ∠ B A T = 90^{\circ} - (1)

Similarly,

∠ CB A = 90^{\circ}

(angle inscribed in a semicircle is

90^{\circ}

)

△ A BC

∠ BC A + ∠ CB A + ∠ C A B = 180^{\circ} \Rightarrow ∠ BC A + ∠ C A B = 90^{\circ} - (2)

Equating

(1)

(2)

we have

∠ O A B + ∠ B A T = ∠ A CB + ∠ C A B \Rightarrow ∠ B A T = ∠ A CB (∵ ∠ C A B = ∠ O A B)

Hence proved

Was this solution helpful?

150

Report

One destination for complete JEE/NEET preparation

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our maths tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	In the adjoining figure. If $A B$ is a chord of the circle with centre $O, A OC$ is a diameter and $A T$ is the tangent at $A$ . Prove that $∠ B A T = ∠ A CB$
Answer Type	Text solution:1
Upvotes	150

In the adjoining figure. If AB is a chord of the circle with centre O,AOC is a diameter and AT is the tangent at A. Prove that ∠BAT=∠ACB

Text solutionVerified

Practice questions from similar books

In the adjoining figure. If $A B$ is a chord of the circle with centre $O, A OC$ is a diameter and $A T$ is the tangent at $A$ . Prove that $∠ B A T = ∠ A CB$