Q. 27
If the lengths of the sides BC, CA and AB of a ΔABC are a, b and c respectively and AD is the bisector of ∠A then find the lengths of BD and DC.
Answer :
Given that ΔABC is the triangle whose sides are AB = c, AC = b, BC = a
And AD is the bisector of ∠A.
We know that altitude bisects the opposite side.
So, let BD = DC = x.
Since AD bisects ∠A,
AC/AB = CD/DB
Substituting the given values,
b/c = CD/(a-CD)
Cross multiplying,
⇒ b( a – CD) = c (CD)
⇒ ba – b(CD) = c (CD)
⇒ ba = CD (b + c)
⇒ CD = ba/ (b + c)
Since CD = BD,
BD = ba/ (b + c)
BD = ba/(b + c) and DC = ba/(b + c)
Rate this question :
How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
RELATED QUESTIONS :
Prove that the internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.
RS Aggarwal - MathematicsIn the given figure, each one of PA, QB and RC is perpendicular to AC. If AP = x, QB = z, RC = y, AB = a and BC = b, show that 
.
If in two 
then
In the given figure, DE || BC such that AD = x cm, DB = (3x + 4) cm, AE = (x + 3) cm and EC = (3x + 19) cm. Find the value of x.
If ΔABC ~ ΔDEF such that 2AB = DE and BC = 6 cm, find EF.
RS Aggarwal - MathematicsΔABC ~ ΔDEF and their perimeters are 32 cm and 24 cm respectively. If AB = 10 cm then DE = ?
RS Aggarwal - MathematicsMatch the following columns:
The line segments joining the midpoints of the sides of a triangle form four triangles, each of which is
RS Aggarwal - MathematicsIn the given figure, O is the point of intersection of two chords AB and CD such that OB = OD and ∠AOC = 45°. Then, ∠OAC and ΔODB are
If in ΔABC and ΔPQR, we have 
then
