In ΔABC, D is a point on side BC such that ∠ADC = ∠BAC. If CA = 15cm and CD = 9 cm, then CB (in cm) = ?
Answer & explanation
Correct answer: option 2
We have,
CA = 15 cm and CD = 9 cm
In ΔCAB and ΔCDA,
∠BAC = ∠ADC (Given)
∠ACB = ∠ACD (Common)
So, ΔCAB ∼ ΔCDA (by AA similarity)
Then, \(\frac{CA}{CB}\) = \(\frac{CD}{CA}\)
= \(\frac{15}{CB}\) = \(\frac{9}{15}\)
= CB = (15 × 15)× \(\frac{1}{9}\)= 25 cm