Point X is on line AC such that AX = 3 CX = 12. If

Question

Point X is on line AC such that AX = 3 CX = 12. If <ABC = <BXA = 90 degrees, then what is BX?

I'm having a really hard time drawing this out.  Is there an easy equation to use for this that won't include drawing it?

Reiny · Accepted Answer

I suspect this is a question in the topic of circles.

If I draw any triangle on the diameter of a circle, then the angle subtended by that diameter must be 90°

So draw a semicircle with a diameter of 15 , (your 3+12 parts of AX and CX )
Since BX is an altitude (it says it is 90°)
BX^2 = 3*12 = 36
BX = √36 = 6