Problem:
Let △XOY be a right-angled triangle with m∠XOY=90∘. Let M and N be the midpoints of legs OX and OY, respectively. Given that XN=19 and YM=22, find XY.
Answer Choices:
A. 24
B. 26
C. 28
D. 30
E. 32 Solution:
Let OM=a and ON=b. Then
192=(2a)2+b2 and 222=a2+(2b)2
Hence
5(a2+b2)=192+222=845
It follows that
MN=a2+b2​=169​=13
Since △XOY is similar to △MON and XO=2⋅MO, we have XY=2⋅MN=26​ .
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