In ΔABC, D is a point on side BC such that ∠ADC= ∠BAC. If CA = 12 cm, CD = 8 cm, then CB (in cm) = ?
Answer & explanation
Correct answer: option 1
Considering \(\Delta \)ACB and \(\Delta \)CDA
\(\angle\)ADC = \(\angle\)BAC (given)
\(\angle\)ACD = \(\angle\)ACB (common)
Thus, by AA postulate
\(\Delta \)CAB is similar to \(\Delta \)CDA
⇒ \(\frac{CA}{CB}\) = \(\frac{CD}{CA}\)
⇒ \(\frac{12}{CB}\) = \(\frac{8}{12}\)
⇒ CB = \(\frac{12\; × \;12}{8}\) = 18 cm.
Therefore, CB is 18 cm.