Question

A chord of a circle is equal to the radius of the circle. Find the angles subtended by the chord at a point on the minor arc and also at a point on the major arc. ​

Answer 1

Que:- A chord of a circle is equal to the radius of the circle. Find the angles subtended by the chord at a point on the minor arc and also at a point on the major arc.

Ans:-

Given:- A circle with chode AB

AB = radius of circlet

Let C be a point on the minor arc

& D be a point on the major arc

To Find:- Angle subtended by a chord at a point in the minor arc, i.e ∠ACB

& Angle subtended by a chord at a point in the major arc, i.e ∠ADB

Construction :- Join AO & OB

Explanation:- In ∆OAB

AB=AO=OB = radius

.•. OAB is a equilateral triangle.

= ∠AOB=60°. (All angles of equilateral

triangle is 60°)

Arc ADB makes ∠AOB at centre & angle ∠ADB at point D ( Angles subtended by the arc or

at the centre is double the

angle subtended by it at

any other point)

So, ∠AOB= 2∠ADB

60° = 2∠ADB

2∠ADB = 60°

∠ADB = 1/2 × 60°

= 30°

Also, ADCB forms a cyclic Quadrilateral.

So, ∠ADB + ∠ACB = 180°

30° + ∠ACB = 180°

∠ACB = 180°-30°

∠ACB = 150°

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