Question

a circle is to be drawn passing through the ends of a line 5 cm long and the angle on the circle on one side of the line should be 80 degree.what should be the radius of the circle?

Answer 1

Answer:

3.89 m

Step-by-step explanation:

Let, AB is a chord of a circle with center at O and has radius r (See the attached diagram).

Length of AB=5 cm. (GIven)

The angle on the circle on one side of AB is ∠AOB =80° (Given)

If we draw a perpendicular OC on AB from center O, then OC will bisect AB at C and also the ∠AOB will be bisected by OC.

So, AC= CB =5/2 cm. =2.5 cm.

And ∠AOC = ∠COB =(80/2)° =40°

Now take ΔOCB where, Sin ∠COB= CB/OB { Since, OC⊥AB}

⇒ Sin 40°= 2.5/r {Since, OA=OB= r}

⇒ r=2.5/Sin 40° =3.89 m (Approximate)

Therefore, the radius of the circle is 3.89 m. (Answer)