ABC is an isosceles right angled triangle having C 90 deg If D is any point on AB then AD2 BD2 is e...........

Quantitative Aptitude (CGL) Coordinate Geometry

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?ABC is an isosceles right angled triangle having ?C = 90°. If D is any point on AB, then AD2+ BD2 is equal to

CD²

2CD²

3CD²

4CD²

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Explanation:

?ABC is a right angle triangle. In which ∠C=90° And D is a point on AB such that D is perpendicular on AB.
Let AC = BC = a
∴AB^2=AC^2+BC^2=a^2+a^2
AB=a^2
∴BD=AD=a√2/2=a/√2
Now In ?ACD
=AC^2=CD^2+AD^2
a^2=CD^2+a^2/2
a^2−a^2/2=CD^2
a^2/2=CD^2
CD^2=a^2/2
2CD^2=a^2
and AD^2+BD^2=(a/√2)^2+(a/√2)^2
=a/√2+a/√2=a^2
∴2CD^2=AD^2+BD^2