triangle ABC has D a point on side BC. Points E and F are on sides AB and AC such that DE and DF are the angle bisectors of angle ADB and angle ADC respectively. Find the value of (AE)/(EB) cdot (BD)/(DC) cdot (CF)/(FA) .

Liberty Page 2022-09-23 Answered
A B C has D a point on side BC. Points E and F are on sides AB and AC such that DE and DF are the angle bisectors of A D B and A D C respectively. Find the value of A E E B B D D C C F F A
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Answers (1)

Mckayla Carlson
Answered 2022-09-24 Author has 7 answers
Step 1
In A D B, angle bisector DE divides AC in ratio of adjacent sides:
A E E B = A D D B
Step 2
Similarly A C D:
C F A F = C D A D
Therefore B D D C A E E B C F F A = B D D C A D B D C D A D = 1
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