Question

Given that AE is a tangent of the circle with the center at B, BC = 3.5, and AE = 24, which is the length of EC? (image attached) http://assets.openstudy.com/updates/attachments/4fa86daee4b059b524f467ea-bdboy0-1336438197775-517a968caaaeec05ce2332fd0b424d1d.gif


A. 7
B. 13
C. 25
D. 49

Answer 1

you have a right triangle.... the chord AC is a diameter

tangents and a radius intersect at right angles so angle EAB = 90

BC = 3.5 so AC = 7 (2 radii in a diameter)


EC is found by Pythagoras' theorem

\[EC^2 = AE^2 + AC^2\]

\[EC^2 = 24^2 + 7^2\]

you can do the rest

Answer 2

thanks