D is a point on the side BC of triangle ABC such that ∠ADC=∠BAC. If CA =12 cm and BC = 16 cm, then the length of CD is:
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Correct answer: D
Explanation
The correct answer is Option 4 i.e. 9 cm.
Given: ∠ADC = ∠BAC
⇒ Triangles ABC and ADC are similar (AA similarity)
So, CA / CD = BC / CA
⇒ 12 / CD = 16 / 12
⇒ CD = (12×12) / 16 = 144 / 16 = 9 cm