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

11-43.

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

 

 

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