Question

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Answer 1

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Answer 2

Answer:

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Given - ABC is a triangle where angle ABC <90 degree and AD is perpendicular to BC.

To prove - AC ² = AB ² + BC ² - 2BC × BD

Prove - In right triangle ADB

By Pythagoras Theorem,

AB²=AD²+BD² ------ ( i )

In right triangle ADC

By Pythagoras theorem,

AC²=AD²+CD² ------ ( ii )

From equation ---- ( ii )

AC²=AD²+CD²

AC²=AD²+(BC-CD)² ( As CD=BC-BD )

AC²=AD²+BD²+BC²-2×BC×BD

Putting AD²+BD²=AB² from equation (i)

AC² = AB² + BC² - 2×BC×BD

HENCE PROOVED.......

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