CAT 2025 Slot 3 QA Question 3: In $ riangle ABC$, $AB = AC = 12$ cm and $D$ is a point on side $BC$ such that $AD = 8$ cm. If $AD$ is extended to a point $E$ such that $\angle ACB = \angle AEB$, then the length, in cm, of $AE$ is

Question

In $	riangle ABC$, $AB = AC = 12$ cm and $D$ is a point on side $BC$ such that $AD = 8$ cm. If $AD$ is extended to a point $E$ such that $\angle ACB = \angle AEB$, then the length, in cm, of $AE$ is

Accepted Answer

Since $AB = AC$, triangle $ABC$ is isosceles. Also, $\angle AEB = \angle ACB$, so $A$, $B$, $C$ and $E$ lie on the same circle.
Point $D$ is the intersection of the two chords $AE$ and $BC$ of this circle. Hence, by the intersecting chords theorem,
$AD 	imes DE = BD 	imes DC$
Now use Stewart’s the

In △ABC\triangle ABC△ABC, AB=AC=12AB = AC = 12AB=AC=12 cm and DDD is a point on side BCBCBC such that AD=8AD = 8AD=8 cm. If ADADAD is extended to a point EEE such that ∠ACB=∠AEB\angle ACB = \angle AEB∠ACB=∠AEB, then the length, in cm, of AEAEAE is

In $\triangle ABC$ , $AB = AC = 12$ cm and $D$ is a point on side $BC$ such that $AD = 8$ cm. If $AD$ is extended to a point $E$ such that $\angle ACB = \angle AEB$ , then the length, in cm, of $AE$ is