Q13 of 57 Page 66

In given figure, if ∠ACB = ∠CDA, AC = 8 cm and AD = 3cm, then find BD.

Given,

AC = 8 cm,


AD = 3 cm and ∠ACB = ∠CDA



From figure,


∠CDA = 90°


∴ ∠ACB = ∠CDA = 90°


In right angled ∆ADC,


AC2 = AD2 + CD2


⇒ (8)2 = (3)2 + (CD)2


CD2 = 64 – 9 = 55


⇒ CD = √55 cm


In ∆CDB and ADC.


∠BDC = ∠AD [each 90°]


∠DBC = ∠DCA [each equal to 90°-∠A]


∴ ∠CDB ∼ ∆ADC


Then,



⇒ CD2 = AD × BD



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