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Question
If ABC is an isosceles triangle and D is a point of BC such that AD ⊥ BC, then
Options
AB2 − AD2 = BD.DC
AB2 − AD2 = BD2 − DC2
AB2 + AD2 = BD.DC
AB2 + AD2 = BD2 − DC2
Solution
Given: ΔABC is an isosceles triangle, D is a point on BC such that `AD ⊥ BC`
We know that in an isosceles triangle the perpendicular from the vertex bisects the base.
∴ BD = DC
Applying Pythagoras theorem in ΔABD
`AB^2=AD^2+BD^2`
`⇒ AB^2-AD^2=BD^2`
`⇒ AB^2-AD^2=BDxxBD`
Since `BD =DC`
`⇒ AB^2-AD^2=BD xxDC`
Hence correct answer is `a`
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