Question

Two vertices of an equilateral triangle A and B are on a circle and third vertex O is at the center. What is the measure of angle APB shown in the figure?​

Answer 1

Given :-

• Two vertices of an equilateral triangle A and B are on a circle and third vertex O is at the center.

To find :-

• ∠APB = ?

Solution :-

from figure , we can see that, we have ,

→ ∆AOB is an equilateral ∆ .

So,

→ ∠AOB = ∠OAB = ∠OBA = 60° . ( Each angle of an equilateral triangle is equal to 60° .)

Now, we have ,

→ ∠AOB = 60° = Angle at centre .

→ ∠APB = Angle at circumference .

→ AB is a common chord.

we know that, The angle subtended by an arc at the centre is twice the angle subtended at the circumference .

Therefore,

→ ∠AOB = 2∠APB

→ 60° = 2∠APB

→ ∠APB = (60°/2)

→ ∠APB = 30° .(Ans.)

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