Question

in the given figure O is centre of a circle if angle abc = 100 degree and Angle AOC equal to 90 degree then angle BAC is​

Answer 1

Given:

O is centre of a circle if angle AOB = 100 degrees and angle AOC equal to 90 degree

To find:

angle BAC

Solution:

We know that,

The angle subtended by an arc of a circle at its centre is double the angle it subtends anywhere on the circle's circumference

So, we get

∠BOC = 2 ∠BAC ..... (i)

∠AOB + ∠AOC + ∠BOC = 360° ..... [sum of all angles in a circle]

on substituting the values of ∠AOB & ∠AOC from the given figure, we get

⇒ 100° + 90° + ∠BOC = 360°

⇒  190° + ∠BOC = 360°

⇒ ∠BOC = 360° - 190°

⇒ ∠BOC = 170° ..... (ii)

From (i) & (ii), we get

170° = 2 × ∠BAC

⇒ ∠BAC = $\frac{170\°}{2}$

⇒ ∠BAC = 85°

Thus, ∠BAC = 85°.

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Also View:

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Answer 2

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