Question

a chord of a circel is equal to the radius of the circel . find the angel subtended by the chord at a point on the minor arc. fig also see plz​

Answer 1

Step-by-step explanation:

Given:-

Achord of a circel is equal to the radius of the circle.

To find :-

Find the angel subtended by the chord at a point on the minor arc.

Solution:-

( See the above attachment)

Let O is the centre of the circle .

AB is the Chord .

AB=Radius of the circle.

C is the point in the minor arc.

D is the point in the major arc

Angle subtended by the chord at C in the minor arc = angle ACB

Angle subtended by the chord at D in the major arc = angle ADB

On joining OA and OB we get ∆OAB in which

OA = OB = AB = radius

=>all the three sides are equal.

=>∆OAB is an equilateral triangle

= Each angle is equal to 60°

angle AOB = angle OAB = angle OBA = 60°

major arc ADB makes an angle ADB

we know that

"angle subtended by an arc at the centre is double angke subtended by at any other point on it".

=>angle AOB = 2( angle ADB)

= 60° =2 (angle ADB)

=>angle ADB = 60°/2

= angle ADB = 30°

and

all the vertices A,B,C,D are lie on the same circle.

=>ABCD is a cyclic quadrilateral

We know that

The sum of opposite angles is 180°

=>angle ADB +angle ACB = 180°

=>30°+angle ACB = 180°

=>angle ACB = 180°-30°

angle ACB = 150°

Answer:-

Angle subtended by the arc at the point in minor arc = 150°

and in the major arc = 30°

Used formulae:-

• "angle subtended by an arc at the centre is double angke subtended by at any other point on it".
• The sum of opposite angles is 180°

Answer 2

Step-by-step explanation:

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