Question

1.A chord of a circle is equal to its radius.find the angle subtended by this chord in the major segment
2.ABCD is a quadrilateral in which AB is the largest side and CD is the shortest side.prove that angle is greater than angle A and angle D is greater than angle B

Answer 1

1) Chord of the circle is equal to its radius. 

Hence the triangle formed by two radii and the chord is an equilateral triangle. 

The angle subtended at the centre is 60 degrees

Angle subtended by the chord in the major segment is half of the angle at the centre. That means, it measures 30 degrees

2) 

Answer 2

Answer:

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.

∠AOC=60°

Also, ∠ACB= 1/2×∠AOB= 1/2 ×60°=30°

ACBD is a cyclic quadrilateral,

∠ACB+∠ADB=180° ∣ Opposite angles of cyclic quadrilateral

⇒∠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.

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