In the figure S and T trisect the side QR of a right triangle PQR. Prove that 8PT^2 = 3PR^2 + 5PS^2 @AviJainClasses

Uploaded January 2020 | Updated September 2026, 2 weeks ago

In the figure S and T trisect the side QR of a right triangle PQR. Prove that 8PT^2 = 3 PR^2 + 5 PS^2.
triangles class 10.

Here are some of the important questions from outside the book with their links as well:
1) In the figure, AB, PQ and CD are parallel to each other. AB = x units, CD = y units and PQ = z units. Prove that 1/x + 1/y = 1/z.
youtu.be/aPbkE7nkzLg
2) ABC is a right triangle, right angled at C. If p is the length of the perpendicular from C to AB and AB = c, BC = a and CA = b, then prove that 1/p^2 = 1/a^2 + 1/b^2
youtu.be/0-GzPT_7jOs
3) In the figure DEFG is a square. angle BAC = 90. Prove that DE^2 = BD x EC.
youtu.be/6zP0zbdak40
4) If A is the area of a right angled triangle and b is one of the sides containing the right angle, prove that the length of the altitude on the hypotenuse is 2Ab/ square root of (b^4 + 4A^2)
youtu.be/mD2l1kWCTac
5) In the given figure, M is the mid point of side CD of a parallelogram ABCD. The line BM is drawn intersecting AC at L and AD produced at E. Prove that EL=2BL
youtu.be/FdqW4ygozOI
6) In the figure S and T trisect the side QR of a right triangle PQR. Prove that 8PT^2 = 3 PR^2 + 5 PS^2
youtu.be/aGamdzMGinU
7) In triangle ABC, P and Q are points on AB and AC such that PQ is parallel to BC. Prove that median AD bisects PQ.
youtu.be/72JRjp4wnbA
8) Prove that three times the sum of squares of sides of a triangle is equal to four times the sum of the squares of its medians.
youtu.be/1hXsIUVryK0
9)OB is the perpendicular bisector of the line segment DE. FA is perpendicular to OB and FE intersects OB at point C. Prove that 1/OA+1/OB=2/OC.
youtu.be/9oFkhS9HERI
10) The side BC of a triangle ABC is bisected at D. O is any point on AD. BO and CO produced meet AC and AB at E and F respectively. AD is produced to X so that D is the mid point of OX. Show that FE is parallel to BC.
youtu.be/jDF_ZcpQkq4

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