In a \Delta ABC, AC=12 \text{ cm}, AB=16 \text{ cm} and AD is the bisector of \angle A. If BD=4 \text{ cm}, then what is DC equal to?

Explanation

By the Angle Bisector Theorem, the angle bisector of a triangle divides the opposite side into segments proportional to the adjacent sides: \frac{AB}{AC} = \frac{BD}{DC}. Substituting the values: \frac{16}{12} = \frac{4}{DC}. Thus, DC = \frac{12 \times 4}{16} = 3 \text{ cm}.

Related questions on Geometry

• In a triangle ABC, \angle A = 30^\circ, AB = 7 cm and AC = 12 cm. What is the area of the triangle ABC?
• ABC is a triangle right angled at B. D is a point on AC such that BD is perpendicular to AC. If AB = p and BC = \sqrt{3}p, then what is BD...
• The difference between an interior angle and an exterior angle of a regular polygon is 120°. What is the number of sides of the polygon?
• An angle q is exactly one-fourth of its complementary angle. What is the value of angle q?
• The sides of a triangle are 11 cm, 60 cm and 61 cm. What is the area of the triangle formed by joining the mid-points of the sides of the tr...