2019 AIME I Problems/Problem 6
Problem 6
In convex quadrilateral 
side 
is perpendicular to diagonal 
, side 
is perpendicular to diagonal 
, 
, and 
. The line through 
perpendicular to side 
intersects diagonal at 
with 
. Find 
.
Solution (Similar triangles)
(writing this, don't edit)
![[asy] size(250); real h = sqrt(98^2+65^2); real l = sqrt(h^2-28^2); pair K = (0,0); pair N = (h, 0); pair M = ((98^2)/h, (98*65)/h); pair L = ((28^2)/h, (28*l)/h); pair P = ((28^2)/h, 0); pair O = ((28^2)/h, (8*65)/h); draw(K--L--N); draw(K--M--N--cycle); draw(L--M); label("K", K, W); label("L", L, NW); label("M", M, NE); label("N", N, E); draw(L--P); label("P", P, S); dot(O); label("O", shift((1,1))*O, NNE); [/asy]](http://latex.artofproblemsolving.com/3/1/5/3153978d9d14bfc7b0604e2984235f322eafb8bd.png)
Video Solution
Video Solution: https://www.youtube.com/watch?v=0AXF-5SsLc8
See Also
| 2019 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
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