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Question

In the figure given above, AC is the diameter. AB, BC, AD, DC are chords of the circle.

AD = BC = 3 cm.

Then, ΔABCΔADC


A

True

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B

False

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Solution

The correct option is A

True


As the angles made by the diameter at the circumference is 90, so ΔABC and ΔADC are right angle triangles, right angled at B and D respectively.

In the figure given above, consider

In ΔABCIn ΔADCAB2+BC2=AC2AD2+DC2=AC2AB2+32=5232+DC2=52AB2+2599+C2=25AB2=16DC2=259AB2=42DC2=16AB=4DC=4

In ΔABC and ΔADC
BC = AD (given)
AB = DC (AB = DC = 5 cm)
AC = AC (common side)
ΔABCADC (by SSS criterion of congruency)


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