Waste less time on Facebook — follow Brilliant.
×

Pre-RMO 2014/15

Let \(XOY\) be a triangle with \(\angle XOY = 90^\circ\). Let \(M\) and \(N\) be the midpoints of legs \(OX\) and \(OY\), respectively. Suppose that \(XN = 19\) and \(YM = 22\). What is \(XY\)?


This note is part of the set Pre-RMO 2014

Note by Pranshu Gaba
3 years ago

No vote yet
1 vote

Comments

Sort by:

Top Newest

is XY 26????

Nitish Deshpande - 3 years ago

Log in to reply

Let \(XM=MO=a\) and \(ON=NY=b\)

By applying PT, we get

\(4a^{2}+b^{2}=19^{2} \rightarrow Eq.1\)

\(a^{2}+4b^{2}=22^{2} \rightarrow Eq.2\)

Eq.1+Eq.2

\(a^{2}+b^{2}=\frac{19^{2}+22^{2}}{5}=13^{2}\)

\( \Rightarrow \sqrt{4a^{2}+4b^{2}}=XY=\sqrt{4× 169}=\boxed{26}\)

Aneesh Kundu - 3 years ago

Log in to reply

Length of XY is 26

Moumik Maitra - 2 years, 10 months ago

Log in to reply

XY = 26

KahYeen Lai - 2 years, 10 months ago

Log in to reply

XY=26

KahYeen Lai - 2 years, 10 months ago

Log in to reply

26

Unity 002 - 2 years, 10 months ago

Log in to reply

26

Sudharshan Sharma - 2 years, 10 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...