UPSC CDS I 2025 Mathematics Paper

Given:
AB=2cm,BC=4cm,AC=3cm
Formula used:
Angle bisector theorem: If a bisector of an angle divides the opposite side of a triangle, the ratio of the divided parts equals the ratio of the other two sides.
BD∕DC=AB∕AC
Calculations:
In △ABC,
AD is the bisector of ∠A
So, BD∕DC=AB∕AC=2∕3
Since, BC=4cm
So, BD=2∕5×4=8∕5cm
Now, In △ABD
BE is the bisector of ∠B
So, BD∕AB=ED∕AE
⇒(8∕5)∕2=ED∕AE
⇒4∕5=ED∕AE
⇒5∕4=AE∕ED
So, AE:ED=5:4