CAT (QA) PYQs

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

ABCD is a rectangle with sides AB = 56 cm and BC = 45 cm, and E is the midpoint of side CD. Then, the length, in cm, of radius of in circle of $\triangle$ADE is

From an interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the three perpendiculars is $s$. Then the area of triangle is