In a circle of radius 6cm a chord is drawn 3cm from the center. Calculate the angle subtended by the chord at the center of the circle
To find the angle subtended by the chord at the center of the circle, you can use the formula:
θ = 2 * arcsin (c/2r)
Where:
θ = the angle subtended by the chord at the center
c = length of the chord
r = radius of the circle
In this case, the length of the chord is 3cm and the radius of the circle is 6cm. Plugging these values into the formula, we have:
θ = 2 * arcsin (3/2*6)
= 2 * arcsin (1/4)
≈ 2 * 14.48°
≈ 28.96°
Therefore, the angle subtended by the chord at the center of the circle is approximately 28.96°.
To calculate 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, c is the length of the chord, and r is the radius of the circle.
In this case, the chord is 3 cm from the center, so c = 3 cm, and the radius is 6 cm, so r = 6 cm.
Now we can substitute these values into the formula to solve for θ:
θ = 2 * arcsin(3 / (2 * 6))
= 2 * arcsin(0.25)
≈ 2 * 0.2527
≈ 0.5054 rad
To convert the angle from radians to degrees, we can multiply by 180/π:
θ ≈ 0.5054 * (180/π)
≈ 28.96 degrees
Therefore, the angle subtended by the chord at the center of the circle is approximately 28.96 degrees.
Draw the circle and the chord.
Draw a radius perpendicular to the chord.
If the angle subtended by the chord is θ, then you can see that
cos(θ/2) = 3/6 = 1/2
Now you can find θ.