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Home > CCG > Chapter 11 > Lesson 11.2.1 > Problem 11-85


The length of chord in is mm. If the , find the length of . Draw a diagram.  


Draw a diagram and label with all known values.

Use to find the length of the circle's radius. Then calculate the circumference of the entire circle () and find the length of the arc as a fraction of the whole circle.

 is isosceles.  because both are radii.

Find the measures of the other two angles:
Find the length of the radius either by using the Law of Sines, or by dividing the triangle into two equal right triangles and using trigonometry ratios.

, then  and 

Using the Law of Sines:

Using right triangles:

Circle, with center, D, points, A, &, B, line segments from, D, to, A, from D, to, B, from, A, to, B, angle, A, D, B, labeled 32 degrees, chord, A, B, labeled 9 mm.

A circle with the center, D, and two points on the circumference, A & B. The triangle A, B, D has a central angle at D, 32 degrees. The length of A, B, is 9 millimeters. The triangle is is cut in half by a line, D, E, drawn from D perpendicular to line A, B, at E. A, E is 4.5 millimeters. Angle A, D, E, is 16 degrees.