Q3 of 141 Page 447

In the given figure, BOC is a diameter of a circle and AB = AC. Then, ∠ABC = ?

Given: BOC is the diameter of the circle


AB = AC


Here, BAC forms a semicircle.


We know that angle in a semicircle is always 90


BAC = 90


Here ABC = ACB (since angles opposite equal sides are equal in a triangle)


We know that sum of all the angles in the triangle is 180


That is


ABC + ACB + BAC = 180


⇒ 2 × ABC + BAC = 180


⇒ 2 × ABC + 90 = 180


⇒ 2 × ABC = 180 – 90


⇒ 2 ×ABC = 90


⇒ ABC = 45

More from this chapter

All 141 →
1

The radius of a circle is 13 cm and the length of one of its chords is 10 cm. The distance of the chord from the centre is

 2

A chord is at a distance of 8 cm from the centre of a circle of radius 17 cm. The length of the chord is

 4

In the given figure, O is the centre of a circle and ∠ACB = 30°. Then, ∠AOB = ?

 5

In the given figure, O is a centre of a circle. If ∠OAB = 40° and C is a point on the circle, then ∠ACB = ?