Home
Class 12
MATHS
Let A B C be a triangle with /B=90^0 . L...

Let `A B C` be a triangle with `/_B=90^0` . Let AD be the bisector of `/_A` with D on BC. Suppose AC=6cm and the area of the triangle ADC is `10c m^2dot` Find the length of BD.

Text Solution

Verified by Experts

From angle bisector theorem,

`(r)/(6) = (p)/(q)`
`rArr qr = 6p` ..(1)
Now, area of `DeltaADC = 10 cm^(2)`
`(1)/(2) (DC) (AB) = 10`
`(1)/(2) (q) (r) = 10`
`qr = 20`
From (1), 20 = 6p
`rArr p = (20)/(6) = (10)/(3)`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise 5.1|12 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise 5.2|8 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise ARCHIVES (MATRIX MATCH TYPE )|1 Videos

  • PROPERTIES OF TRIANGLE, HEIGHT AND DISTANCE

    CENGAGE|Exercise Question Bank|15 Videos

Similar Questions

Explore conceptually related problems

Given a right triangle with /_A =90^@ . Let M be the mid-point of BC. If the inradii of the triangle ABM and ACM are r_1 and r_2 then find the range of r_1/r_2

In a Delta ABC , Adis the bisector of angle BAC . If AB=8 cm, BD=6 cm and DC=3 cm. The length of the side AC is

If Delta ABC ~ Delta DEF such that area of Delta ABC " is " 9 cm^(2) and the area of Delta DEF " is " 16 cm^(2) and BC=2.1 cm. Find the length of EF.

Let ABC be an equilateral triangle, let KLMN be a rectangle with K, L on BC , M on AC and N on AB. Suppose AN//NB = 2 and the area of triangle BKN is 6. The area of the triangle ABC is -

Let ABC be a triangle with /_A=45^0dot Let P be a point on side BC with PB=3 and PC=5. If O is circumcenter of triangle ABC, then length OP is sqrt(18) (b) sqrt(17) (c) sqrt(19) (d) sqrt(15)

Let ABC be a triangle with b = 5 , c = 11 if the medium AD is perpendicular to AC , then a =

If an a triangle A B C , b=3ca n d C-B=90^0, then find the value of tanB

ABC is a right angled triangle with angle B = 90 ^@ , a=6 cm if the radius of the circumcircle is 5 cm then the area of Delta ABC is

In a Delta ABC, AB = 52, BC = 56, CA = 60 . Let D be the foot of the altitude from A and E be theintersection of the internal angle bisector of /_BAC with BC. Find the length DE.

Let A B C be a triangle with A B=A Cdot If D is the midpoint of B C ,E is the foot of the perpendicular drawn from D to A C ,a n dF is the midpoint of D E , then prove that A F is perpendicular to B Edot