Question

Hey Guys ♥♥✌✌.

Please explain the Appolonius Theorem and give constructions and proof.

:-)​

Answer 1

Hope it helps u

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Answer 2

Apollonius theorem can be proved by applying the extension of Pythagoras theorem for Obtuse & acute triangle…

GIVEN: A triangle ABC , AM is one of the medians. ie M is the mid point of BC. & MB = MC . If <AMC is obtuse angle, < AMB has to be acute.

REQUIRED TO PROVE:

AC² + AB² = 2AM² + 2BM²

CONSTRUCTION: draw AD Perpendicular to BC.

PROOF: In Obtuse triangle AMC

AC² = AM² + MC² + 2 MC * MD ………. (1)

In acute triangle AMB

AB² = AM² + MB² - 2 MB * MD ……………. (2)

By adding (1) & (2) , since MC = MB

AC² + AB² = 2AM² + 2 MB²

[ Hence Proved]