Question

A chord if a cirle of radius 6cm is making an angle 60 degrees at the center Find the length of the chord

Answer 1

Answer:

The ∆OAB

OA = OB

Then, it will become an isosceles triangle

We know that,

In an isosceles triangle equal sides opposite angles are also equal.

Let the angle be 'y'

Now,

angle OAB = angle OBA

AB = chord

Let the chord be 'x'

By using angle sum property

60° + y + y = 180°

2y = 180° - 60°

2y = 120°

y = 120°/2

y = 60°

Now,

All angles = 60°

Then it is acute angled triangle

We know that

In a acute angle triangle all sides and angles are equal

OA = 6cm

OB = 6cm

AB = 6cm = x

${\mathsf \pink{length \: of \: chord = 6cm }}$