1963 AHSME Problems/Problem 39
Problem 39
In lines and are drawn so that and . Let where is the intersection point of and . Then equals:
Solution
Draw line , and let , , and , so and . Because and share an altitude, Because and share an altitude, Thus, , and since , , which is answer choice .
Solution 2 (Mass Geometry)
Let the mass of point , , , , and be , , , , and respectively. By mass geometry theorems, we have Focusing on the line segment , using mass geometry theorems, we have and which leads to . For line segment , similarly, we got Substituting and back to the equation we obtained at the beginning, we got: which gives us the answer choice . -nullptr07
See Also
1963 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 38 |
Followed by Problem 40 | |
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