CPM Homework Help : GC Problem 11-43

Find the area and circumference of $⊙C$ 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.

Step 1:

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

Therefore $\frac{2}{4} = \frac{3}{x} \rightarrow x=6$

Step 2:

Since you now know that $x = 6$ , you can determine the diameter and radius of the circle.

Hint:

Radius $= 4$

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.

Answer:

Area $= 50.27$ square units
Circumference $= 25.13$ units