Question

In a circle of diametre 40 cm, the length of a chord is 20 cm. Find the length of a chord is 20 cm. Find the length of minor are of the chord

Answer 1

$\Large{\underline{\underline{\bf{Solution :}}}}$

☯ Given :

Diameter of circle = 40 cm

Radius = $\sf{\frac{\cancel{40}}{\cancel{2}}}$ = 20 cm

Length of chord = 20 cm

$\rule{200}{1}$

☯ To Find :

We have to find the minor arc of the chord.

$\rule{200}{1}$

☯ Solution :

Since, triangle is inside the circle. So, it is equilateral triangle.

And we know that,

$\small{\star{\boxed{\sf{Angle \: of \: equilateral \: triangle = 60^{\circ}}}}}$

$\therefore \: \theta$ = 60°

$\rule{150}{2}$

Now, we know that,

$\Large{\implies{\boxed{\boxed{\sf{l = r \theta}}}}} \\ \\ \bf{\dag \: \: \:Putting \: values} \\ \\ \bf{\rightarrow l = 20 \times 60 \: \: \: radian} \\ \\ \sf{\rightarrow l = 120 \: \: \: radian} \\ \\ \bf{Converting \: radian \: measure \: into \: degree} \\ \\ \sf{\rightarrow l = \cancel{120} \times \frac{\pi}{\cancel{180}}} \\ \\ \sf{\rightarrow l = \frac{20 \pi}{3}} \\ \\ \Large{\implies{\boxed{\boxed{\sf{l = \frac{20 \pi}{3}}}}}} \\ \\ \sf{\therefore \: length \: of \: minor \: arc = \frac{20 \pi}{3}}$