ABC is a triangle and D is a point on the side BC. If BC = 12 cm

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

1. 5 cm
2. 6 cm
3. 8 cm
4. 9 cm

Answer

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.