Home › UP Board Class 10 › mathematics › Triangles › In triangle ABC, AD bisects angle A and meets BC…
In triangle ABC, AD bisects angle A and meets BC at D. If AB = 6 cm, AC = 9 cm and BC = 10 cm, then BD equals
A3 cm
B6 cm
C5 cm
D4 cm
Answer & Solution
Correct answer: D. 4 cm
1. By the angle bisector theorem, BD/DC = AB/AC = 6/9 = 2/3.
2. Let BD = 2k, DC = 3k. Then 2k + 3k = 10, so k = 2.
3. Hence BD = 2k = 4 cm.
_Source: NCERT Class 10 Mathematics, Ch 6 "Triangles", §6.3_
Related questions
In triangle ABC, AB squared + BC squared = AC squared and AB = BC. The angles of the trianTriangles ABC and DEF are similar with AB = 4 cm, BC = 5 cm, CA = 6 cm and EF = 7.5 cm. ThIn a quadrilateral ABCD where AB is parallel to CD and the diagonals AC and BD intersect aABC is an equilateral triangle of side 2a. The length of its altitude isThe sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 60 cm. The area ofIn triangle ABC, AD is perpendicular to BC. Given AB = 7 cm, AC = 25 cm, BD = 5 cm, the vaTwo similar triangles have areas 81 sq cm and 144 sq cm. The ratio of their corresponding In an isosceles triangle ABC with AB = AC = 13 cm and BC = 10 cm, the altitude from A to B