Question

AB is a chord of the radius 5cm. The major arc AYB subtends an angle of 240 degree at the center. Find the length of the chord AB.

Find the distance of the chord from the center O of the circle.
Find the length of the minor arc AYB

Answer 1

Consider the figure.

Given,

AB is equal to the radius of the circle.

In △OAB,

OA=OB=AB= radius of the circle.

Thus, △OAB is an equilateral triangle.

and ∠AOC=60°.

Also, ∠ACB=

2

1

∠AOB=

2

1

×60°=30°.

Since, ACBD is a cyclic quadrilateral,

∠ACB+∠ADB=180° ....[Opposite angles of cyclic quadrilateral are supplementary]

⇒∠ADB=180°−30°=150°.

Thus, angle subtend by the chord at a point on the minor arc and also at a point on the major arc are 150° and 30°, respectively