Difference between revisions of "1960 IMO Problems/Problem 4"
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Construct the line <math>l_3</math> parallel to <math>l_2</math> so that the distance between <math>l_2</math> and <math>l_3</math> is <math>h_b</math> and <math>M_a</math> lies between these lines. <math>B</math> lies on <math>l_3</math>. Then <math>B=l_1\cap l_3</math>. | Construct the line <math>l_3</math> parallel to <math>l_2</math> so that the distance between <math>l_2</math> and <math>l_3</math> is <math>h_b</math> and <math>M_a</math> lies between these lines. <math>B</math> lies on <math>l_3</math>. Then <math>B=l_1\cap l_3</math>. | ||
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+ | ==Video Solution== | ||
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+ | https://youtu.be/M0_UdvxH890 | ||
==See Also== | ==See Also== | ||
{{IMO7 box|year=1960|num-b=3|num-a=5}} | {{IMO7 box|year=1960|num-b=3|num-a=5}} | ||
+ | [[Category:Olympiad Geometry Problems]] | ||
+ | [[Category:Geometric Construction Problems]] |
Latest revision as of 00:43, 2 January 2023
Contents
[hide]Problem
Construct triangle , given , (the altitudes from and ), and , the median from vertex .
Solution
Let , , and be the midpoints of sides , , and , respectively. Let , , and be the feet of the altitudes from , , and to their opposite sides, respectively. Since , with , the distance from to side is .
Construct with length . Draw a circle centered at with radius . Construct the tangent to this circle through . lies on .
Draw a circle centered at with radius . Construct the tangent to this circle through . lies on . Then .
Construct the line parallel to so that the distance between and is and lies between these lines. lies on . Then .
Video Solution
See Also
1960 IMO (Problems) | ||
Preceded by Problem 3 |
1 • 2 • 3 • 4 • 5 • 6 • 7 | Followed by Problem 5 |