Question

A triangle ABC is inscribed in a circle and the bisectors of the angles meet the circumference at X,Y and Z. The angles of triangle XYZ are respectively_________

Answer 1

A) 90, 60, 30
B) A/2 , B/2 , C/2
C) 90-A/2 , 90-B/2 , 90-C/2
D) B/2,A/2 , A/2-B/2

Answer 2

Use the fact that an angle subtended by an arc at the circumference is always the same. i.e.:

angle PRQ = angle PSQ
so:

angle AXY = angle ABY = B/2
angle AXZ = angle ACZ = C/2
therefore angle YXZ = B/2 + C/2 = (B+C)/2

follow the same procedure for the other angles.

the answer I get, however, does not seem to match any of the ones you have listed, so maybe I have got the diagram wrong - can you please clarify?