In the figure, PQRS is a parallelogram with PQ = 16 cm and QR = 10 cm, L is a point on PR such that RL : LP = 2 : 3. QL produced meets RS at M and PS produced at N. Find the lengths of PN and RM.

In △PQR, ∠Q = 90° and QM is perpendicular to PR. Prove that :

(i) PQ² = PM × PR

(ii) QR² = PR × MR

(iii) PQ² + QR² = PR²

In the given figure, ΔABC and ΔAMP are right angled at B and M respectively.

Given AC = 10 cm, AP = 15 cm and PM = 12 cm.

(i) Prove that : ∆ABC ~ ∆AMP.

(ii) Find AB and BC.

In triangle ABC, AD is perpendicular to side BC and AD² = BD × DC.

Show that angle BAC = 90°.