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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


Team Careers360 3rd Jan, 2024
Answer (1)
Team Careers360 18th Jan, 2024

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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