in a circle, the angle subtended by the chord at the circumference is 32 degrees.if the radius of the circle is 12cm, calculate the length of the chord
find other two angles
2 A + 32 = 180
A = 74 degrees
sin A / R = sin 32/c
so
c = 12 sin 32 / sin 74 = 12 * 0.53 / 0.96 = 6.6 cm
To calculate the length of the chord in a circle, we can use the following formula:
Chord Length = 2 * Radius * sin(angle/2)
In this case, the given angle subtended by the chord at the circumference is 32 degrees, and the radius of the circle is 12 cm. Using the formula, we can calculate the length of the chord as follows:
Chord Length = 2 * 12 cm * sin(32/2)
= 2 * 12 cm * sin(16)
≈ 2 * 12 cm * 0.2756
≈ 6.6144 cm
Therefore, the length of the chord is approximately 6.6144 cm.
To find the length of the chord, we need to use the property of circles that states an inscribed angle is equal to half the measure of the arc it intercepts.
Given:
- Angle subtended by the chord at the circumference = 32 degrees.
- Radius of the circle = 12 cm.
Step 1: Find the measure of the intercepted arc.
Since the angle subtended by the chord at the circumference is 32 degrees, the intercepted arc would be twice that measure.
Intercepted arc = 2 * 32 = 64 degrees.
Step 2: Calculate the circumference of the circle.
The formula for finding the circumference of a circle is given by C = 2πr, where C is the circumference and r is the radius.
C = 2 * π * 12 = 24π cm.
Step 3: Find the proportion of the intercepted arc to the total circumference.
To find the proportion of the intercepted arc, divide the measure of the intercepted arc by the total circumference.
Proportion = Intercepted arc / Total circumference
Proportion = 64 / (24π)
Proportion ≈ 0.847
Step 4: Calculate the length of the chord.
The length of the chord can be found by multiplying the proportion of the intercepted arc to the total circumference by the circumference of the circle.
Length of chord = Proportion * Circumference
Length of chord = 0.847 * 24π cm
Length of chord ≈ 20.235 cm.
Therefore, the length of the chord is approximately 20.235 cm.