Question

a chord of a circle is equal to the radius of the circle then the angle subtended by the chord at the centre of a circle​

Answer 1

ANSWER

if chord is equal to radius

then now think that it form Equivaletral triangle.

Having all sides equal which imply having all angles equal. let it be x

x+x+x = 180 { by angle sum property }

x = 180/3

x = 60 degree

so angle is 60 degree

hope it helps

Answer 2

Solution :-

GIVEN

• Chord = Radius of circle.

To Find

• Angle subtended by chord at centre.

Construction

• Draw 2 radius from each end of chord .

• Join then to centre.

Now it's given that

Radius = Chord = Radius .

→ It shows that the triangle is equilateral triangle.

As we know that the each angle of equilateral triangle measure 60° .

So the angle subtended by chord at the centre is of 60 °

Another Way

As we know that in a triangle angle opposite to equal sides are also equal .

Here each side is equal.

So it's each angle is also equal . Let's assume each angle as x .

By interior angle sum property.

x + x + x = 180°

3x = 180°

x = 60°