In the given figure, $△ A B C$ is an isosceles triangle with $A B = A C$ and $O$ is the centre of the circle. If $∠ A O B = α$ and $∠ A O C = β$ , then which of the following is true?

$α = 2 β$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$α = \frac{β}{2}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$α = β$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$α = 3 β$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C
$α = β$

$A B$ and $A C$ are equal chords of the circle.

Angle subtended by chord $A B$ at the centre = $∠ A O B = α$

Angle subtended by chord $A C$ at the centre= $∠ A O C = β$ .

We know that equal chords subtend equal angles at the centre.

$\Rightarrow ∠ A O B = ∠ A O C$

i.e., $α = β$

Suggest Corrections

Similar questions

In the given figure, $△ A B C$ is an isosceles triangle with $A B = A C$ and $O$ is the centre of the circle. If $∠ A O B = α$ and $∠ A O C = β$ , then which of the following is true?

A B C

is a triangle inscribed in a circle with centre

O

. Let

α = ∠ B A C

, where

45^{o} < α < 90^{o}

. Let

β = ∠ B O C

. Which one of the following is correct?

Q. A parallelogram is constructed on the vectors

a = 3 α - β, b = α + 3 β,

| α | = | β | = 2

and angle between

α

and

β

\frac{π}{3},

then length of a diagonal of the parallelogram is

Q. In the figure chord AB and CD when produced meet at point P. If

∠ A O C = θ, ∠ B O D = α

then prove that

∠ A P C = \frac{θ - α}{2}

( O is the centre of the circle )

Q. The roots of the quadratic equation

(x + β) (x - α) = 0

are:

Join BYJU'S Learning Program

In the given figure, △ABC is an isosceles triangle with AB=AC and O is the centre of the circle. If ∠AOB=α and ∠AOC=β, then which of the following is true?

The correct option is C α=β AB and AC are equal chords of the circle. Angle subtended by chord AB at the centre =∠AOB=α Angle subtended by chord AC at the centre= ∠AOC=β. We know that equal chords subtend equal angles at the centre. ⇒∠AOB=∠AOC i.e., α=β

In the given figure, $△ A B C$ is an isosceles triangle with $A B = A C$ and $O$ is the centre of the circle. If $∠ A O B = α$ and $∠ A O C = β$ , then which of the following is true?