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प्रश्न
In the figure, if ∠ACB = ∠CDA, AC = 8 cm and AD = 3 cm, find BD.
उत्तर
Given,
AC = 8 cm,
AD = 3 cm
And ∠ACB = ∠CDA
From figure,
∠CDA = 90°
∠ACB = ∠CDA = 90°
In right angled ΔADC,
AC2 = AD2 + CD2
⇒ (8)2 = (3)2 + (CD)2
⇒ 64 – 9 = CD2
⇒ CD = `sqrt(55)` cm
In ΔCDB and ΔADC,
∠BDC = ∠ADC ...[Each 90°]
∠DBC = ∠DCA ...[Each equal to 90° – ∠A]
∴ ΔCDB ∼ ΔADC
Then, `("CD")/("BD") = ("AD")/("CD")`
⇒ CD2 = AD × BD
∴ BD = `("CD"^2)/("AD")`
= `(sqrt(155))^2/3`
= `55/3` cm
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