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Home > GC > Chapter 11 > Lesson 11.1.3 > Problem 11-43

11-43.

Find the area and circumference of at right. Show all work.  

Circle, with center, c, has a horizontal dimeter and a chord on the right side of the circle intersecting. The segments around the point of intersection are labeled as follows: top, 4, right, 2, bottom, 3, left, unknown.

The two triangles are similar, which means the ratios of corresponding sides are equal.

Therefore 

Since you now know that , you can determine the diameter and radius of the circle.

Radius 

Added to the circle, segments connecting each end of the diameter with an end of the chord, creating 2 triangles, with the unknown portion of the diameter labeled as x.

Area square units
Circumference units