Question : ABC is an isosceles triangle having $\angle$ C = 90$^\circ$, if D is any point on AB, then AD2 + BD2 is equal to:
Option 1: CD2
Option 2: 2CD2
Option 3: 3CD2
Option 4: 4CD2
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Correct Answer: 2CD 2
Solution :
Given that ABC is an isosceles triangle with $\angle$ C = 90$^\circ$.
Construct a circle of radius $r$ circumscribing triangle ABC with AB as diameter as $\angle$C will be an angle in a semicircle.
Since D can be any point, take it as the center of the circle.
By construction, AD = BD = CD = $r$
So, AD
2
+ BD
2
= 2$r^2$
or, AD
2
+ BD
2
= 2CD
2
Hence, the correct answer is 2CD
2
.
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