Question

What is the angle subtended at the centre of a circle of radius 5 cm buy a chord of length 5 cm

Answer 1

Answer:

We know that the arc length l of a sector of an angle θin a circle of radius r is



It is given thatand length. Substituting these value in above equation,



Hence, the angle subtended at the centre of circle is

Answer 2

Answer:

$60^{\circ}$

Explanation:

We are given that a circle of radius 5 cm and chord of length 5 cm

We have to find the angle subtended at the centre of circle

Let O be the center of given circle and $\theta$ be the angle subtended at the centre by a chord

OA=OB=5 cm

AB= 5cm

Draw a OP is perpendicular bisector  to AB

Then AP=PB and angle AOP=BOP=$\frac{\theta}{2}$

AP=PB=$\frac{5}{2} cm$

We know that

$Sin\theta=\frac{Perpendicular }{Hypotenuse}$

$Sin \frac{\theta}{2}=\frac{AP}{AO}$

$sin \frac{\theta}{2}=\frac{\frac{5}{2}}{5}$

$sin\frac{\theta}{2}=\frac{5}{2\times 5}$

$sin \frac{\theta}{2}=\frac{1}{2}$

We know that $sin 30^{\circ}=\frac{1}{2}$

Therefore,$sin\frac{\theta}{2}=sin 30^{\circ}$

$\frac{\theta}{2}=30^{\circ}$

$\theta=30\times 2=60^{\circ}$

Hence, the angle subtended at the center by the chord =$60^{\circ}$