Question

Bisectors of∠ B and ∠C of ∆ ABC intersect each other in point X.

Line AX intersects side BC in point Y.

AB = 5, AC = 4, BC = 6 then find AX/ XY.​

Answer 1

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Asked on December 27, 2019 by

Amita Sankhla

In the figure, bisectors of ∠B and ∠C of ΔABC intersect each other in point X. Line AX intersects side BC in point Y. AB=5, AC=4, BC=6, then find

XY

AX

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ANSWER

Since, the bisectors of a triangle are concurrent, then AY is the bisector of ∠A.

Then from angle-bisector property we get, [Using the bisector of ∠C ]

XY

AX

=

YC

AC

........(1).

Again, since AY is the bisector of ∠A then

YC

BY

=

AC

AB

or,

YC

BY

=

4

5

or,

YC

BY+YC

=

4

5+4

or,

YC

BC

=

4

9

or, YC=

3

8

.

From (1) we get,

XY

AX

=

2

3

.

Answer 2

I hope my answer is really helpful for you