Difference between revisions of "2021 JMPSC Accuracy Problems/Problem 6"

(Created page with "==Problem== In quadrilateral <math>ABCD</math>, diagonal <math>\overline{AC}</math> bisects both <math>\angle BAD</math> and <math>\angle BCD</math>. If <math>AB=15</math> and...")
 
(Solution)
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==Solution==
 
==Solution==
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Notice that since <math>\overline{AC}</math> bisects a pair of opposite angles in quadrilateral <math>ABCD</math>, we can distinguish this quadrilateral as a kite.
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<math>\linebreak</math>
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With this information, we have that <math>\overline{AD}=\overline{AB}=15</math> and <math>\overline{CD}=\overline{BC}=13</math>.
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Therefore, the perimeter is <cmath>15+15+13+13=\boxed{56}</cmath>
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<math>\square</math>
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<math>\linebreak</math>
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~Apple321

Revision as of 23:48, 10 July 2021

Problem

In quadrilateral $ABCD$, diagonal $\overline{AC}$ bisects both $\angle BAD$ and $\angle BCD$. If $AB=15$ and $BC=13$, find the perimeter of $ABCD$.

Solution

Notice that since $\overline{AC}$ bisects a pair of opposite angles in quadrilateral $ABCD$, we can distinguish this quadrilateral as a kite.

$\linebreak$ With this information, we have that $\overline{AD}=\overline{AB}=15$ and $\overline{CD}=\overline{BC}=13$.

Therefore, the perimeter is \[15+15+13+13=\boxed{56}\] $\square$

$\linebreak$ ~Apple321

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