Triangle ABC is a right triangle. D is the midpoint of hypotenuse AC

Question

Triangle ABC is a right triangle. D is the midpoint of hypotenuse AC. BE is tangent to DC. What is DE?

1) AB=12
2) BE=9

Can someone please help me with this question??

Thank you!!

chetan2u · Answer

Hi,
i believe the answer should be C....
the answer cannot be A,B or D as a single value cannot deduce any other value here..
in any right triangle with two sides given, where two sides could be any altitude or one side, two sides etc... most of the values can be deduced..
here too, all three sides can be found with given two values.. hypotenuse comes out as a negative value or 36..
so it is 36, lly other values can be deuced...

cjcj · Answer

How do you get the 36 number? Sorry...

chetan2u · Answer

1)let hyp AC=x, so BC=x^2-12^2, AB is given as 12...
so  area = 12*\sqrt{x^2-12^2}/2

2) now if hyp is taken as base the alt BE is given as 9..
so area will be 9*x/2..

the areas have to be same..
 9*\frac{x}{2}=12*\sqrt{x^2-12^2}/2 
you will get x as \frac{48}{\sqrt{7}}

AdlaT · Answer

Can anyone please draw a figure for this question?

GMATBusters · Answer

What is meant by " BE is tangent to DC "?

Please explain

gvij2017 · Answer

BE is tangent to DC...what does this mean?
Is BE is arc and where does E lie?

Triangle ABC is a right triangle. D is the midpoint of hypotenuse AC

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