# Radius of a Circle and Lengths of Arcs

1.If an arc 70mm long subtends an angle of pi over 4 radians at the centre what is the radius of the circle?

2.A chord of length 26mm is drawn in a circle of 35mm diameter. What are the lengths of the smaller and larger arcs into which the circumference is divided?

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#### Solution Preview

Please see the attached Word document for the solutions to these exercises.

1. If an arc 70mm long subtends an angle of pi over 4 radians at the centre what is the radius of the circle?

This problem is simple if you use the formula for finding the arc length given the angle and the radius. If an arc of length s on a circle of radius r subtends an angle , measured in radians, then:

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#### Solution Summary

The solution finds the radius of a circle and lengths of arcs. The circumferences divided are given.

Arcs and chords of a circle.

Using the diagram at right:

1. If the diameter of circle M is 20, and the length of line segment DF is 12, what is the length of segment MJ?

2. If the measure of arc BFE is 80 degrees, then what is the measure of angle BME?

3. If there were an imaginary angle ACB, what would the measure of that angle be? (Hint: Remember that a line is an angle with a measure of 180 degrees, or that a circle has a total arc measure of 360 degrees.)

4. If angle EMA has a measure of 100 degrees, what is the measure of arc EDA?

5. If I had an imaginary line from M to H, with a length of 15, and told you that line segment HI had a length of 9, what would the radius of circle M be?

6. Imagine there is a line segment AD, and a line segment BF. If the measure of angle DAB is 60 degrees, what is the measure of angle DFB?

7. If angle EMA is 95 degrees, what is the measure of angle BME?

8. If I drew a line segment from A to C, and the radius of circle M was 1, what would line segment AC be?

9. If the diameter of circle M is 12, what would the length of MI be?

10. If imaginary triangle DJE were a 30-60-90 triangle, with angle EDJ as the 30 degree angle, and chord DF had a length of 18, what would the length of line segment DE be?

See attached file for full problem description.

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