in triangle CAR, AT bisects <CAR and T lies on CR. If AC=8, AR=12, and CR=12. find CT.?

Question

a) 4.8
b) 7.2
c) 12.2
d) cannot be determined

Answer 1

The angle bisector divides the third side into segments that are in the same ratio as the other two sides, so
RT/CT = 12/8 = 3/2

Since RT = 12 - CT, we have:
(12 - CT)/CT= 3/2

Cross multiplying gives:
2(12-CT) = 3(CT)
24 - 2CT = 3CT
24 = 5CT
CT = 24/5 = 4.8

Drawing the diagram will make the algebra clearer.

Answer 2

a?