In ΔABC, D is a point on side BC such that ∠ADC = ∠BAC. If CA = 12 cm, CB = 8 cm, then CD is equal to:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 18 cm.
In ΔADC and ΔBAC:
∠C = Common
∠ADC = ∠BAC
By AA criterion, Both the triangles are similar.
Let us assume ∠DAC = α
Then, ∠ABC = α (Similar triangles)
AC/BC = 12/8 = 5/2
Then,
x : 12 = 3 : 2 (By similar traiangle property)
⇒ x = 18 cm