In a Triangle Abc, Ac > Ab, D is the Midpoint Bc, and Ae ⊥ Bc. Prove That: Ab2 + Ac2 = 2ad2 + 1 2 Bc 2 - Mathematics

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In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AB2 + AC2 = 2AD2 + `(1)/(2)"BC"^2`

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Solution


We have ∠AED = 90°
∴ ∠ADE < 90° and ∠ADC > 90°
i.e. ∠ADE is acute and ∠ADC is obtuse.

Adding (i) and (ii), we have
AC2 + AB2 = AD2 + BC x DE + `(1)/(4)"BC"^2  + "AD"^2 - "BC" xx "DE" + (1)/(4)"BC"^2`

⇒ AB2 + AC2 = `2"AD"^2 + (1)/(2)"BC"^2`.    ....(iii)

  Is there an error in this question or solution?
Chapter 17: Pythagoras Theorem - Exercise 17.1

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Frank Class 9 Maths ICSE
Chapter 17 Pythagoras Theorem
Exercise 17.1 | Q 15.3

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