Triangles Examples and Solutions

In a ∆ABC, AD is the bisector of ∠BAC. If AB = 8 cm, BD = 6 cm and DC = 3 cm. Find AC

A 13m long ladder reaches a window of a building 12m above the ground. Determine the distance of the foot of the ladder from the building. 

If ABC is a right triangle right-angled at B and M, N are the mid-points of AB and BC respectively, then 4(AN² + CM²) =

∆ABC is such that AB = 3cm, BC = 2cm, CA = 2.5cm. If ∆ABC ~ ∆DEF and EF = 4cm, then perimeter of ∆DEF is ______.

D and E are respectively the points on the sides AB and AC of a triangle ABC such that AD = 2 cm, BD = 3 cm, BC = 7.5 cm and DE || BC. Then, length of DE (in cm) is ______.

The incircle of an isosceles triangle ABC, in which AB = AC, touches the sides BC, CA and AB at D, E and F respectively. Prove that BD = DC.

In the given figure, each of PA, QB, RC and SD is perpendicular to l. If AB = 6 cm, BC = 9 cm, CD = 12 cm and PS = 36 cm, then determine PQ, QR and RS.

If ∆ABC is an equilateral triangle such that AD ⊥ BC, then AD² =