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

- 5 cm
- 6 cm
- 8 cm
- 9 cm

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

AC^{2} = 12 × 3 = 36

AC = 6 cm

**The correct option is B.**

- ABC is a triangle with AB = BC and D is an interior point
- ABCD is a square. X is the mid-point of AB
- There are 24 equally spaced points lying on the circumference of a circle
- A circle is inscribed in a given square and another circle is circumscribed about the square
- PQR is a non-isosceles right-angled triangle, right angled at Q