In a triangle ABC, a point P is chosen on side −−→AB such that AP:PB=1:4 and a point Q is chosen on side −−→BC such that CQ:QB=1:3. Line segment −−→CP and −−→AQ intersect at M. If the ratio MCPC is expressed as a rational number in the lowest term as ab, then b−a equals

In a triangle ABC, a point P is chosen on side −−→AB such that A

1.	In a triangle ABC, a point P is chosen on side −−→AB such that AP:PB=1:4 and a point Q is chosen on side −−→BC such that CQ:QB=1:3. Line segment −−→CP and −−→AQ intersect at M. If the ratio MCPC is expressed as a rational number in the lowest term as ab, then b−a equals
Answer» In a triangle $A B C,$ a point $P$ is chosen on side $- - \to A B$ such that $A P : P B = 1 : 4$ and a point $Q$ is chosen on side $- - \to B C$ such that $C Q : Q B = 1 : 3.$ Line segment $- - \to C P$ and $- - \to A Q$ intersect at $M .$ If the ratio $\frac{M C}{P C}$ is expressed as a rational number in the lowest term as $\frac{a}{b},$ then $b - a$ equals