Question

given: ea & ec are common external tangents of g and b. af=55, dg=9, & eg=41. what is the measure of ce?

Answer 1

Answer on Question #48884 – Math – Geometry

Given: $EA$ and $EC$ are common external tangents of $G$ and $B$. $AF = 55, DG = 9, EG = 41$. What is the measure of $CE$?

Solution

We can see that $CE = AE$ and $FG = DG$ (radius of small circle).

According to Pythagorean Theorem:

$$EF = \sqrt{EG^2 - FG^2} = \sqrt{EG^2 - DG^2}.$$

The measure of $CE$ is

$$CE = AE = AF + EF = AF + \sqrt{EG^2 - DG^2} = 55 + \sqrt{41^2 - 9^2} = 95.$$

Answer: 95.

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