Question

In the given figure PA, QB and RC are each perpendicular to AC. If AP = x, BQ = y and CR = z, then prove that 1/x + 1/z = 1/y

In the adjoining figure, AD/BD = AE/EC and ∠BDE = ∠CED, prove that △ABC is an isosceles triangle.

In the adjoining figure, △CAB is a right triangle, right angled at A and AD ⊥ BC. Prove that △ADB ~ △CDA. Further, if BC = 10 cm and CD = 2 cm, find the length of AD.

In the adjoining figure, ABCD is a trapezium in which XY ∥ AB ∥ CD. If AX = 2/3 AD, then CY : YB =

State the basic proportionality theorem. Use the theorem to do the following : In △ABC, AD is the angle bisector of angle A. BA is produced to E such that CE ∥ AD. Prove that BD/DC = BA/AC.