Question

the two chords AB and CD of a circle are at equal distance from the centre O. if angle angle AOB= 60° and CD=6 cm. then calculate the length of the radius of the circle​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given:

→AB and CD are the two chords of the circle.

→OM=ON

→∠AOB=60°

→CD=6cm

To Find:

➩ The radius of the circle.

Solution:

We have,

CD=6cm

We know that,

→The two chords of the circle are equidistant from its centre must have the same length.

The two chords of the circle are equidistant from its centre must have the same length. Thus, the two chords AB and CD will be of equal length.

CD=AB

AB=6cm (as CD=6cm)

Now,

AO=BO (Radius of a circle are always equal)

∠OAB=∠OBA (Angles opposite to equal sides are always equal.)

Let ∠OAB=∠OBA= x

In △AOB

x+x+60°=180°(The sum of all the angles of a triangle is 180°)

so,

x+x+60°=180°

2x+60°=180°

2x=180°-60°

2x=120°

$x =\frac{120}{2}$

x=60°

so

∠OAB=∠OBA=60°

Also ∠AOB=60°

So this implies △AOB is an equilateral triangle as the measure of each and every angle is 60°

We know ,

AB=AO=BO (sides of equilateral △ are always equal.

AO=6cm ( as AB=OA)

so AO=BO=CO=DO=6cm (Radius of a circle are always equal)