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?

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