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In the given figure, angle ACB=90^(@) a...

In the given figure, ` angle ACB=90^(@) and CD bot AB`. Prove that `CD^(2)=BD*AD`

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GIVEN `A Delta ABC` in which `angle ACB=90^(@) and CD bot AB`.
TO RPOOVE `CD^(2)= BD*AD`.
PROOF In right `Delta ADC`, we get have `angle 1+ angle 2=90^(@)`
In right `Delta ACB`, we have
` angle 1+angle 3=90^(@)`
`:. angle 1+ angle 2= angle 1+ angle 3 rArr angle=2 angle 3`.
In `Delta ABC and Delta CDB`, we have
`angle2= angle3`
` and angle ADC = angleCDB= 90^(@)`
`:. Delta ADC ~ Delta CDB=90^(@)`
`:. (AD)/(CD)=(CD)/(BD)`
Hence, `CD^(2)=BD*AD`.
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