Question

chord of a circle is 13.2 cm long and circles radius is 9.4 find the angle subtended by the chord at the centre of the circle

Answer 1

To find the angle subtended by a chord at the center of a circle, we can use the formula:

θ = 2 * arcsin (c / 2r)

where θ is the angle subtended by the chord, c is the length of the chord, and r is the radius of the circle.

Step 1: Substitute the given values into the formula

θ = 2 * arcsin (13.2 / (2 * 9.4))

Step 2: Simplify the equation

θ = 2 * arcsin (13.2 / 18.8)

Step 3: Use a calculator or a math table to find the value of arcsin

arcsin (13.2 / 18.8) = 0.636 radians

Step 4: Multiply the value obtained by 2

0.636 * 2 = 1.27 radians

Final Answer: The angle subtended by the chord at the centre of the circle is 1.27 radians or 72.8 degrees

Answer 2

ForTheTriangleABOtofindthelengthr

Wehave

sin(

2

α

)=

hypotenuse

opposite

=

OA

AB

=

9.4

6.6

=0.70212

whereAB=

2

13.2

=6.6cm

2

α

=sin

−1

(0.70212)

thenweoptain=

α=44.6°×2

=89.2°