1967 AHSME Problems/Problem 32
Contents
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
(Diagram not to scale)
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 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 31 |
Followed by Problem 33 | |
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