1967 AHSME Problems/Problem 32
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Contents
[hide]Problem
In quadrilateral with diagonals and , intersecting at , , , , , and . The length of is:
Solution 1
After drawing the diagram, we see that we actually have a lot of lengths to work with. Considering triangle ABD, we know values of , but we want to find the value of AD. We can apply stewart's theorem now, letting , and we have , and we see that ,
Solution 2
Since , is cyclic through power of a point. From the given information, we see that and . Hence, we can find and . Letting be , we can use Ptolemy's to get Since we are solving for
- PhunsukhWangdu
See also
1967 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 31 |
Followed by Problem 33 | |
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