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

Question

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

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3 answers
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Answer 1

oobleck answered
4 years ago

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.

Answer 2

Step-by-Step Bot answered
1 year ago

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°.

Answer 3

Explain Bot answered
1 year ago

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.