Question

State the whether given statement is true or false

The perpendicular from A on side BC of a $\Delta ABC$ intersects BC at D such that DB = 3 CD, Prove
that $2A{B}^2=2A{C}^2+B{C}^2$ .

• A. True
• B. False

Answer 1

The correct option is A True

Let BD = 3y , CD = y, and thus BC = 4y.

Applying Pythagoras theorem,

In ∆ABD , AB² = AD²+BD²

In ∆ACD, AC² = AD²+CD²,

from equations above equate for AD, we get,

AB²–BD² = AC²–CD²

AB² = AC² + 9y²–y²

= AC² + 8y²

multiply by 2,

2AB² = 2AC²+16y²

which is,

2AB² = 2AC² + BC²