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Question

In the given figure ABC is a right triangle and right angled at B such that BCA=2BAC.
Show that hypotenuse AC = 2BC.
(Hint : Produce CB to a point D that BC = BD)
1378622_cee6ffc696114f30a9f089fd8694ef14.png

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Solution

In ABD and ABC we have BD=BC
AB=AB [Common]
ABD=ABC=90
By SAS criterion of congruence we get
ABDABC
AD=AC and DAB=CAB [By CPCT]
AD=AC and DAB=x [CAB=x]
Now, DAC=DAB+CAB=x+x=2x
DAC=ACD
DC=AD [Side Opposite to equal angles]
2BC=AD since DC=2BC
2BC=AC Since AD=AC
Hence proved.

1303696_1378622_ans_28358894258f4eadbff364282848643f.PNG

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