Question

Geometry: finding an angle of an inscribed triangle

Answer 1

This is the pic of the circle: http://imgur.com/pk9EN7u

"AB is the diameter of the circle, and the centre is labelled X. C is the circumference of the circle, and CAB = 2*CBA. What's the size of CBA?"

I don't even know how to find CAB, let alone CBA.

Answer 2

Look at < C. It is an angle inscribed in a semi-circle and is a right angle.

By < C, I mean <ACB

Answer 3

Since AB is a diameter, /_C has to be 90. An inscribed angle is half the intercepted arc and we know the arc is 180º because it is half the circle due to AB being the diameter. Now we know m/_CBA+m/_CAB=90. We also know m/_CAB=2m/_CBA so we can plug in 2m/_CBA from the second equation into the first to get m/_CBA+2m/_CBA=3m/_CBA=90 and so m/_CBA=30. That means m/_CAB=60