Trapezoid $ABCD$ has sides $AB=92,BC=50,CD=19,AD=70$ $AB$ is parallel to $CD$ A circle with center $P$ on $AB$ is drawn tangent to $BC$ and $AD$.Given that $AP=\dfrac mn$ (Where $m,n$ are relatively prime).What is $m+n$?
Problem
Source: Bangladesh National Mathematical Olympiad 2015
Tags: geometry, contests, Bdmo, trapezium, angles
safhaqitsme123
25.02.2019 13:29
nice question vai.
Olympus_mountaineer
25.02.2019 14:28
I think this is an $AIME$ problem too.Isn't it?
safhaqitsme123
25.02.2019 17:36
it maybe
safhaqitsme123
25.02.2019 17:38
Can anyone solve this one? I,m having trouble
Olympus_mountaineer
25.02.2019 18:09
safhaqitsme123 wrote: it maybe Because this formate of $m+n$ is very common for $AIME$.
ubermensch
25.02.2019 19:31
1992 AIME problem 9
Olympus_mountaineer
25.02.2019 20:46
ubermensch wrote: 1992 AIME problem 9 My guess was correct!Thanks for the link.
safhaqitsme123
26.02.2019 17:28
i was thinking it to be a AMC10 or AMC12 problem.
Calvera
09.04.2021 19:42
Nice problem for bashers.
pomodor_ap
01.01.2025 09:50
Let $E$ is intersection point of line $AD$ and line $BC$. $EP$ bisects $\angle AEB$, $$AP:PB=EA:EB=DA:BC=7:5$$$\to$ $AP=\dfrac{AP}{AP+PB}\cdot 92=\dfrac{161}{3}$. Answer : $\textbf{164}$.