# Math Help - Geometry problem - using congruence/similarity only

1. ## Geometry problem - using congruence/similarity only

Hi, I'm having problems solving this geometry problem, using congruence and similarity only.

Let ABC be a right angled triangle, with the 90° angle at C. The midpoint of hypotenuse AB is twice as far from side BC as it is from side AC. Find the length of side AC, if AB = 10cm?

First of all, I can't even construct a proper diagram with that info! If someone could attach one, that would be appreciated. Also, how could I solve it using congruence or similarity only?

Thanks, BG

2. Originally Posted by BG5965
Let ABC be a right angled triangle, with the 90° angle at C. The midpoint of hypotenuse AB is twice as far from side BC as it is from side AC. Find the length of side AC, if AB = 10cm?
You can show that $m(CB)=2x~\&~m(CA)=4x$.