Home
Class 12
MATHS
Prove m:n theorem in a Delta ABC, a poin...

Prove m:n theorem in a `Delta ABC`, a point D is taken on side BC such that BD:DC is m:n. Then prove that
(1)`(m+n)cottheta= mcotalpha-ncotbeta`
(2)`(m+n)cottheta= ncotB-mcotC`

Text Solution

Verified by Experts

1)`(BD)/(DC)=m/n`
`/_ADB=180-theta`
`/_ABD=180-(alpha+180-theta)`
`=theta-alpha`.
`In/_ABD`
`(BD)/sinalpha=(AD)/(sin(theta-alpha))`
`In/_ADC`
`(DC)/sinbeta=(AD)/(sin(theta-beta))`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

If l ,\ m,\n are three lines such that l || m\ a n d\ n_|_l , prove that n_|_mdot

In Delta ABC , point M on AB and point N on AC are such that AM = (1)/(4)AC and AN =(1)/(4)AC . Prove that MN =(1)/(4) BC

If m and n are positive quantites , prove that ((mn+1)/(m+1))^(m+1)ge n^(m)

If cos e c\ theta+cottheta=m and cos e c\ theta-cottheta=n , prove that m n=1

If sin(theta+alpha)=nsin(theta-alpha) and n!=-1 ,prove that cottheta=(n-1)/(n+1)cotalpha

If m and n are two distinct numbers such that m >n, then prove that m^2-n^2 ,2mn and m^2+n^2 is a Pythagorean triplet.

If sinx+cosx=m and secx+cosecx=n prove that n(m^2-1)=2m

In any DeltaABC, if D be any points of the base BC such that (BD)/(DC)=m/n and angle ABD =alpha, angle DAC =beta,angle CDA=thetaand AD=x then prove that (m+n) ^(2). x =(m+n) (mb^(2) +nc^(2))-mna^(2)

In any DeltaABC, if D be any points of the base BC such that (BD)/(DC)=m/n and angle ABD =alpha, angle DAC =beta,angle CDA=thetaand AD=x then prove that (m+n) ^(2). x =(m+n) (mb^(2) +nc^(2))-mna^(2)