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Question

In the given figure, if AE = 4 cm and EC = 8 cm, then length of BC is equal to



A

12 cm
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B

4 cm
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C

2 cm
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D

6 cm
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Solution

The correct option is D
6 cm
Given: AE = 4 cm and EC = 8 cm
Let the point of intersection of two circles be P.




In Δ ADE and ΔABC,A=A (Common)ADE=ABC=90

ΔADEΔ ABC (By AA similarity criterion)

AEAC=DEBCAEAE+EC=DEBC44+8=DEBC412=rBCBC=3r..(i)

Now, EC=8cm (Given)EP+PC=8cmr+3r=8 cm (PC=BC=3r and DE=PE=r)4r=8cmr=2cm

BC=3×2=6cm

Hence, the correct answer is option d.

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