AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

In the given figure, O is the centre of a circle, AB is a chord and AT is the tangent at A. If ∠AOB=100⁰, then which of the following is the measure of ∠BAT?

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

40⁰

50⁰

90⁰

100⁰

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Consider the given figure,
Question Image

Given that,
AB is a chord.
AT is the tangent at A.
∠AOB=100⁰
As, AO and BO are the radius of the circle.
Then,

A O = B O

So, ∆AOB is an isosceles triangle.

∴ ∠ OAB = ∠ OBA

Consider ∆AOB,

⇒ ∠ A O B + ∠ O B A + ∠ O A B = 180 ° ⇒ 100 ° + ∠ O A B + ∠ O A B = 180 ° ⇒ 2 ∠ O A B = 80 ° ⇒ ∠ O A B = 40 °

We know that the radius and tangent are perpendicular at their point of contact.

∴ ∠ O A T = 90 ° ⇒ ∠ O A B + ∠ B A T = 90 ° ⇒ ∠ B A T = 90 ° − 40 ° ⇒ ∠ B A T = 50 °

Hence,

∠ B A T

is equal to

50 °

.
Therefore, option 2 is correct.

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!