Place P and the origin and Q at (5,0), A=(1,0)
Its easy to show B=(3/5,4/5) C=(3/5,16,5)
Line L has some slope, m and so equation y=m(x1)
Its a fair amount of work to find points D and E, but knowing A helps.
For D:
x^2+m^2(x1)^1=1
x=(1m^2)/(m^2+1)
y=(2m)/(m^2+1)
For E:
(x5)^2+m^2(x1)^2=16
x=(m^2+9)/(m^2+1)
y=(8m)/(m^2+1)
To find an area formula for DBA, contruct K where segment BD intersects the xaxis. K=((m2)/(m+2),0)
The add the ares of ABK and ADK
After some simplifying the area is
.8(2m1)/(m^2+1)
To find an area formula for ACE, construct F and G on the xaxis under C and E. Then ACE=ACF+FCEGAEG
After a lot of simplifying the area is
6.4(2m)/(m^2+1)
Setting the two areas equal and solving gives
m=1.5
From which each area formula gives the solution: 64/65

Posted by Jer
on 20161119 09:00:48 