top button
Flag Notify
    Connect to us
      Site Registration

Site Registration

If the medians of triangle ABC intersect at P , then evaluate AB^2+AC^2+BC^2/PA^2+PB^2+PC^2

+1 vote
405 views

If the medians of triangle ABC intersect at P , then evaluate 

 AB^2+AC^2+BC^2
----------------
 PA^2+PB^2+PC^2

enter image description here

posted May 1, 2016 by anonymous

Share this puzzle
Facebook Share Button Twitter Share Button LinkedIn Share Button

2 Answers

+1 vote

enter image description here

Median Theorem ----- Va^2+Vb^2+Vc^2 = 3/4(AB^2+AC^2+BC^2)
In this triange --- Va = PA + PA/2 = 3.PA/2
Vb = PB + PB/2 = 3.PB/2
Vc = PC + PC/2 = 3.PC/2
9/4(PA^2+PB^2+PC^2) = 3/4(AB^2+AC^2+BC^2)
(AB^2+AC^2+BC^2) / (PA^2+PB^2+PC^2) = (9/4). (4/3) = 9/3 = 3

answer Aug 25, 2018 by Halil Akansel
0 votes

ans. is - (OC^2)
--------------
(OP^2)

answer May 2, 2016 by Pranali Nikam
Where is the point 'O' in the diagram?
commented May 3, 2016 by Naveen Chopra



Similar Puzzles
0 votes
Triangle ABC has a right angle at B. Let Q be along BC and P be along AB........what is the length of the hypotenuse AC?

Triangle ABC has a right angle at B. Let Q be along BC and P be along AB such that AQ bisects angle A and CP bisects angle C. If AQ = 9 and CP = 8√2, what is the length of the hypotenuse AC?
enter image description here

+1 vote
In a Right angle triangle ABC - AB=3,AC=4 & BC=5. At BC, E is middle point and D is altitude AD. Find distance DE=?

In a Right angle triangle ABC

AB=3,AC=4 & BC=5

at BC,E is middle point and D is altitude AD

Find distance DE=?

it is not a difficult question everyone who know maths ...
Can YOU solve it easily ...... solve it in one line...........or in second..........?

0 votes
Let ABC be a triangle with AB < AC < BC. Let the incentre and incircle of triangle ABC be I and ω, respectively.........

Let ABC be a triangle with AB < AC < BC. Let the incentre and incircle of triangle ABC be I and ω, respectively. Let X be the point on the line BC different from C such that the line through X parallel to AC is tangent to ω. Similarly, let Y be the point on the line BC different from B such that the line through Y parallel to AB is tangent to ω. Let AI intersect the circumcircle of triangle ABC again at P ≠ A. Let K and L be the midpoints of AC and AB, respectively.
Prove that ∠KIL + ∠YPX = 180°.
enter image description here

0 votes
Triangle ABC has AB = BC = 10 and AC = 10√2. The triangle is folded so that point A falls on the midpoint M of BC......

Triangle ABC has AB = BC = 10 and AC = 10√2. The triangle is folded so that point A falls on the midpoint M of BC. The crease endpoints P, Q are along sides AB and AC, respectively.
What is the length of the crease PQ?
enter image description here

0 votes
Triangle ABC has sides AB = 8, BC = 7, and AC = 9. The segments AB and AC...............What is the radius of circle O?

Triangle ABC has sides AB = 8, BC = 7, and AC = 9.
The segments AB and AC are extended and a circle O is constructed exterior to the triangle and is tangent to BC at D and the extended lines through AC and AB at N and M, as shown.
What is the radius of circle O?
enter image description here

...