If `A B C` is a right triangle right-angled at `Ba n dM ,N` are the mid-points of `A Ba n dB C` respectively, then `4(A N^2+C M^2)=` (A) `4A C^2` (B) `5A C^2` (C) `5/4A C^2` (D) `6A C^2`

In a right triangle A B C right-angled at B , if P a n d Q are points on the sides A Ba n dA C respectively, then (a) A Q^2+C P^2=2(A C^2+P Q^2) (b) 2(A Q^2+C P^2)=A C^2+P Q^2 (c) A Q^2+C P^2=A C^2+P Q^2 (d) A Q+C P=1/2(A C+P Q)dot

In Figure, A B C is a right triangle right angled at B and points Da n dE trisect B C . Prove that 8A E^2=3A C^2+5A D^2dot

In a right A B C right-angled at C , if D is the mid-point of B C , prove that B C^2=4\ (A D^2-A C^2) .

A B C is a triangle right angled at B ; a n d\ P is the mid-point of A C . Prove that: P Q\ _|_A B (ii) Q is the mid point of A B P B=P A=1/2A C

A B C is an isosceles triangle in which A B=A Cdot If Da n dE are the mid-points of A Ba n dA C respectively, prove that the points B ,C ,Da n dE are concylic.

Construct a right triangle, right angled at C in which A B=5. 2"\ "c m and B C=4. 6\ c mdot

In right-angled triangle A B C in which /_C=90^@ , if D is the mid-point of B C , prove that A B^2=4\ A D^2-3\ A C^2 .

In Figure, Pa n dQ are the midpoints of the sides C Aa n dC B respectively of A B C right angled at C. Prove that 4(A Q^2+B P^2)=5A B^2 .

A B C is an isosceles triangle in which A B=A C . If D\ a n d\ E are the mid-points of A B\ a n d\ A C respectively, Prove that the points B ,\ C ,\ D\ a n d\ E are concyclic.

In Fig. 4.192, A B C is a right triangle right-angled at B . A D and C E are the two medians drawn from A and C respectively. If A C=5c m and A D=(3sqrt(5))/2c m , find the length of C E . (FIGURE)