Let `A B C D` be a rectangle and `P` be any point in its plane. Show that `A P^2+P C^2=P B^2+P D^2dot`

In Figure, lines A B\ a n d\ C D are parallel and P is any point between the two lines. Prove that /_A B P+/_C D P=\ /_D P B

In Figure, A B C D\ a n d\ P Q R C are rectangles and Q is the mid-point of A C . Prove that D P=P C (ii) P R=1/2\ A C

In Figure, A B C D\ a n d\ P Q R C are rectangles and Q is the mid-point of A C . Prove that D P=P C (ii) P R=1/2\ A C

In A B C ,D is the mid-point of A B ,P is any point of B CdotC Q P D meets A B in Q . Show that a r( B P Q)=1/2a r( A B C)dot

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

The coordinates of A ,B ,C are (6,3),(-3,5),(4,-2) , respectively, and P is any point (x ,y) . Show that the ratio of the area of P B C to that of A B C is (|x+y-2|)/7dot

The coordinates of A ,B ,C are (6,3),(-3,5),(4,-2) , respectively, and P is any point (x ,y) . Show that the ratio of the area of P B C to that of A B C is (|x+y-2|)/7dot

The coordinates of A ,B ,C are (6,3),(-3,5),(4,-2) , respectively, and P is any point (x ,y) . Show that the ratio of the area of P B C to that of A B C is (|x+y-2|)/7dot

The coordinates of A ,B ,C are (6,3),(-3,5),(4,-2) , respectively, and P is any point (x ,y) . Show that the ratio of the area of P B C to that of A B C is (|x+y-2|)/7dot

If a, b, c, d are in A.P. and a, b, c, d are in G.P., show that a^(2) - d^(2) = 3(b^(2) - ad) .