Q. 255.0( 1 Vote )

# If ABC is an isosceles triangle and D is a point on BC such that, then

A. AB^{2} - AD^{2} = BD. DC

B. AB^{2} - AD^{2} = BD^{2} - DC^{2}

C. AB^{2} + AD^{2} = BD. DC

D. AB^{2} + AD^{2} = BD^{2} - DC^{2}

Answer :

Given ABC is an isosceles triangles and AD ⊥ BC.

We know that in an isosceles triangle, the perpendicular from the vertex bisects the base.

∴ BD = DC

We know that the Pythagoras theorem state that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Now, in right triangle ABD,

⇒ AB^{2} = AD^{2} + BD^{2}

⇒ AB^{2} – AD^{2} = BD^{2}

⇒ AB^{2} – AD^{2} = BD (BD)

Since BD = DC,

∴ AB^{2} – AD^{2} = BD (DC)

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