Let `A(p^2,-p),B(q^2, q),C(r^2,-r)` be the vertices of triangle ABC. A parallelogram AFDE is drawn with D,E, and F on the line segments BC, CA and AB, respectively. Using calculus, show that the maximum area of such a parallelogram is `1/2(p+q)(q+r)(p-r)dot`

Let A(1, -1), B(4, - 2) and C(9,3) be the vertices of the triangle ABC . A parallelogram AFDE is drawn with vertices D, E and F on the line segments BC, CA and AB respectively Find the maximum area of parallelogram AFDE .

p A N D q are any two points lying on the sides D C a n d A D respectively of a parallelogram A B C Ddot Show that a r( A P B)=a r ( B Q C)dot

Let P be an interior point of a triangle ABC , Let Q and R be the reflections of P in AB and AC , respectively if Q .A , R are collinear then angle A equals -

If P(–2, 4), Q(4, 8), R(10, 5) and S(4, 1) are the vertices of a quadrilateral, show that it is a parallelogram.

Prove that the figure formed by joining the mid-points of the pair of consecutive sides of a quadrilateral is a parallelogram. OR B A C D is a parallelogram in which P ,Q ,R and S are mid-points of the sides A B ,B C ,C D and D A respectively. A C is a diagonal. Show that : P Q|| A C and P Q=1/2A C S R || A C and S R=1/2A C P Q=S R (iv) P Q R S is a parallelogram.

In Delta P Q R , if P Q=Q R and L ,M and N are the mid-points of the sides P Q ,Q R and R P respectively. Prove that L N=M Ndot

A B C D is a parallelogram. P is the mid-point of A BdotB D\ a n d\ C P intersect at Q such that C Q : Q P=3: 1. If a r\ ( P B Q)=10\ c m^2, find the area of parallelogram A B C D

If G(3,-5,r) is centroid of triangle ABC where A(7,-8,1), B(p,q,5) and C(q+1,5p,0) are vertices of a triangle then values of p,q,r are respectively

The sides AB,BC and AC of a triangle ABC touch a circle with centre O and radius r at P Q,and R respectively.

If G(3, -5, r) is centroid of triangle ABC where A(7, - 8, 1), B(p, q, 5) and C(q + 1, 5p, 0) are vertices of a triangle then values of p, q, r are respectively ...