Question

solve it...............​

Answer 1

Refer to the attachment:

Given

AB = AC

To prove

AB² - AD² = BD × CD

Proof

In ∆ABD & ∆ABC we have:

AD = AD ( common side)

AB = AC ( Given )

<ABD = <ACD ( Opposite angles of equal sides)

So, ∆ABD ≅ ∆ABC {By SAS congruency}

By CPCT, BD = DC ----> (1)

also, <ADB = <ADC

Now, <ADB + <ADC = 180° {Linear pair}

=> <ADB + <ADB = 180°

=> 2<ADB = 180°

=> <ADB = 90°

So, ∆ADB is right angled at <D

By Pythagoras theorem

AB² = AD² × BD²

=> AB² - AD² = BD²

=> AB² - AD² = BD × BD

=> AB² - AD² = BD × CD { from (1) }

Hence Proved

Answer 2

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