In the given figure, O is the centre of the circle. If $∠ A O B = 100^{\circ}$ and $∠ A O C = 90^{\circ}$ , then find $∠ B A C$ .

85^{\circ}

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90^{\circ}

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80^{\circ}

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75^{\circ}

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Solution

The correct option is A $85^{\circ}$
$∠ A O B + ∠ A O C + ∠ B O C = 360^{\circ}$ (sum of all the angles at a point)
$100^{\circ} + 90^{\circ} + ∠ B O C = 360^{\circ}$
$∠ B O C = 170^{\circ}$
$∠ B A C = \frac{1}{2} (∠ B O C) = \frac{1}{2} (170^{\circ}) = 85^{\circ}$
(The angle subtended by an arc of a circle at its centre is twice the angle it subtends anywhere on the circle’s circumference. )

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Similar questions

Q. In the given figure, O is the centre of the circle. If ∠AOB = 100° and ∠AOC = 90°, then find ∠BAC.

In the given figure, $O$ is the centre of a circle. If $∠ A O B = 100^{\circ}$ and $∠ A O C = 90^{\circ}$ , then $∠ B A C = ?$

(a) $85^{\circ}$

(b) $80^{\circ}$

(d) $75^{\circ}$

Q. In the figure, O is the centre of the circle with

∠ A O B = 85^{\circ} a n d ∠ A O C = 115^{\circ}, t h e n ∠ B A C

is :

(i) In figure (1), $O$ is the centre of the circle. If $∠ O A B = 40^{\circ}$ and $∠ O C B = 30^{\circ}$ . Find $∠ A O C$ .

(ii) In figure (2), $A, B$ and $C$ are three points on the circle with centre $O$ such that $∠ A O B = 90^{\circ}$ and $∠ A O C = 110^{\circ}$ . Find $∠ B A C$ .

In the given figure, O is the centre of a circle. If $∠ A O B = 100^{\circ} a n d ∠ A O C = 90^{\circ} t h e n ∠ B A C = ?$

(a) $85^{\circ}$

(b) $80^{\circ}$

(d) $75^{\circ}$

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In the given figure, O is the centre of the circle. If ∠AOB=100∘ and ∠AOC=90∘, then find ∠BAC.

The correct option is A 85∘∠AOB+∠AOC+∠BOC=360∘ (sum of all the angles at a point) 100∘+90∘+∠BOC=360∘ ∠BOC=170∘ ∠BAC=12(∠BOC)=12(170∘)=85∘ (The angle subtended by an arc of a circle at its centre is twice the angle it subtends anywhere on the circle’s circumference. )

In the given figure, O is the centre of the circle. If $∠ A O B = 100^{\circ}$ and $∠ A O C = 90^{\circ}$ , then find $∠ B A C$ .