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Question

A circle has two equal chords AB and AC. Chord AD cuts BC in E. If AC=12 cm. and AE=8 cm, then AD (in cm) is equal to

A
27
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B
24
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C
21
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D
18
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Solution

The correct option is D 18
In ΔACD and ΔACE.
D=B...(angle in the same segment)
B=C...(angle opposite to equal sides)
D=C
A is common.
from AA similarity ΔACD and ΔACE are similar.
ACAE=ADAC
or 128=AD12
or 8AD=12×12
or AD=12×128=18cm
85499_98155_ans_70bb673a4a3c4328b8e1cc91c65ce465.png

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