Book Online Demo

Check Your IQ

Try Test

Courses

If AB and BC are two tangents to a circle with centre $O$ such that $∠ AOC = 120 °$ then find $∠ ABC$ .

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

60 °

40 °

50 °

30 °

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

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

Take Free Test

Detailed Solution

Given that, AB and BC are two tangents to a circle with centre

O

∠ AOC = 120 °

As we can see that OABC is a quadrilateral, where

OA ⊥ BA,

The tangent to the circle at any point is the perpendicular to the radius of the circle that passes through the point of contact

OC ⊥ BC

And,

∠ OAB = 90 °,

∠ OCB = 90 °

Now in quadrilateral OABC,
Sum of all the angles of a quadrilateral is 360°.

∠ ABC + ∠ AOC + ∠ OAB + ∠ OCB = 360 °

∠ ABC + 120 ° + 90 ° + 90 ° = 360 °

∠ ABC = 360 ° - 300 °

∠ ABC = 60 °

Thus, the value of

∠ ABC = 60 °

.
Therefore, option (1) is correct.

Watch 3-min video & get full concept clarity