If ABC is an equilateral triangle and AD ⊥ BC, then AD 2 =

Question

Philoid · Accepted Answer

The given triangle is shown below:

By applying Pythagoras theorem in right angled triangle ADC, we get,

AC² = AD² + DC² [∵ h² = p² + b²]

⇒ AD² = AC² – DC²

⇒ AD² = BC² – DC² [AC = BC, sides of equilateral Δ]

⇒ AD² = (2DC) ² - DC² [BC = 2DC, AD bisects BC]

⇒ AD² = 4DC² - DC²

⇒ AD² = 3DC²

If ABC is an equilateral triangle and AD ⊥ BC, then AD2 =