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Question
In the given figure, ∠ADC = ∠BCA; prove that ΔACB ∼ ΔADC. Hence find BD if AC = 8 cm and AD = 3 cm.
Solution
Given, AC = 8 cm, AD = 3 cm
and ∠ADC = ∠BCA
From the figure in ΔADC and ΔBCA
∠A = ∠A ...(Common)
∠ADC = ∠BCA ...(Given)
So, by AA similarity criteria
ΔADC ∼ ΔBCA
∵ Corresponding sides are in the same ratio
`(AC)/(AD) = (AB)/(AC)`
`8/3 = (AB)/8`
AB = `(8 xx 8)/3`
= `64/3` cm
Now from the figure,
BD = AB – AD
= `64/3 - 3`
= `(64 - 9)/3`
= `55/3`
BD = `18 1/3` cm.
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