Difference between revisions of "2019 AIME I Problems/Problem 6"
(→Solution (Similar triangles)) |
|||
Line 5: | Line 5: | ||
(writing this, don't edit) | (writing this, don't edit) | ||
<asy> | <asy> | ||
− | size( | + | 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> | </asy> | ||
Revision as of 08:53, 15 March 2019
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)
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.