Question

in triangle abc ad is perpendicular to BC prove that AC square equal to a b square + BC square minus 2 BC into BD​

Answer 1

Solution:

We know that Pythagoras theorem

H² =√P²+B²

Now applying this theorem in Triangle ABD we get

AD²+DB² = AB² ⇒ AD² = AB²-DB²² ------(1)

and now applying Pythagoras theorem in Triamgle ADC we get

AD²+DC² = AC²

now using eq (1) we get

AB²-BD²+DC² = AC²

⇒AB²-BD²+(BC-BD)² = AC²

⇒AC² =AB²-BD²+BC²+BD²-2BC×BD = AB²+BC² -2BC×BD

HENCE PROVED AC² = AB²+BC² -2BC×BD