Question

Given:EA and Ec are common external tangents of G and B. DC equals 44, GF equals 7 and EG equals 25. What is the measure of AE?

Answer 1

Given: EA and EC are common external tangents of G and B. DC equals 44, GF equals 7 and EG equals 25. What is the measure of AE?

If EA and EC are common external tangents of G and B, then

1). $\angle BCE = \angle BAE = \angle GDE = \angle GFE = 90{}^{\circ}$

2). AE=CE and ED=EF

Pythagorean theorem for $\Delta FGE$

$EG^{2} = GF^{2} + EF^{2}$ , so

$EF = \sqrt{EG^2 - GF^2} = \sqrt{25^2 - 7^2} = 24,$ so DE=24

Hence $\mathrm{CE} = \mathrm{CD} + \mathrm{DE} = 44 + 24 = 68$ so AE=68

Answer: AE=68