ABC is a triangle and D is a point on the side BC. If BC = 12 cm, BD = 9 cm and ∠ADC = ∠BAC, then the length of AC is equal to
BC = 12 cm, BD = 9 cm
As D is a point on the side BC
BC = BD + CD
CD = 3 cm
In ΔBAC and ΔADC
∠ADC = ∠BAC (Given)
∠C = ∠C (Common angle)
∴ ΔBAC ~ ΔADC (AA similarity criteria)
The ratio of sides is also equal.
BC : AC = AC : CD
AC × AC = BC × CD
AC2 = 12 × 3 = 36
AC = 6 cm
The correct option is B.