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# Geometry question - urgent -maths olypiad tomorrow watch

1. Hey,

I am residing in an Asian country and have my olympiad test tomorrow. I am stuck at this question and I think I will get a similar question in the test.

Would be really grateful for any urgent help!!!

Question:

2. Let ABC be an equilateral triangle and P be a point inside this triangle such that PA= x , PB=y,
PC=z. If z 2 = x2 + y2 , find the length of the sides of triangle ABC in terms of x and y.
2. (Original post by foolzgold)
Hey,

I am residing in an Asian country and have my olympiad test tomorrow. I am stuck at this question and I think I will get a similar question in the test.

Would be really grateful for any urgent help!!!

Question:

2. Let ABC be an equilateral triangle and P be a point inside this triangle such that PA= x , PB=y,
PC=z. If z 2 = x2 + y2 , find the length of the sides of triangle ABC in terms of x and y.

draw perpendiculars from P to sides AB , BC and AC (call them q,r,s)
then say triangle QPA we can find the lenght AQ(by Pythagoras) and QB
AQ+QB=AB which is one side
findling the lenghts of all the three sides by this method ..and equal AB=BC=AC ..also the perpendiculars add up to the height of the equilateral ..

Im not sure if this gets you anywhere just another idea
3. (Original post by rbnphlp)
draw perpendiculars from P to sides AB , BC and AC (call them q,r,s)
then say triangle QPA we can find the lenght AQ(by Pythagoras) and QB
AQ+QB=AB which is one side
findling the lenghts of all the three sides by this method ..and equal AB=BC=AC ..also the perpendiculars add up to the height of the equilateral ..

Im not sure if this gets you anywhere just another idea
thanx for the help, but this method did not work

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