# 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...") |
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==Solution== | ==Solution== | ||

− | + | 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. | |

+ | |||

+ | <math>\linebreak</math> | ||

+ | With this information, we have that <math>\overline{AD}=\overline{AB}=15</math> and <math>\overline{CD}=\overline{BC}=13</math>. | ||

+ | |||

+ | Therefore, the perimeter is <cmath>15+15+13+13=\boxed{56}</cmath> | ||

+ | <math>\square</math> | ||

+ | |||

+ | <math>\linebreak</math> | ||

+ | ~Apple321 |

## Revision as of 23:48, 10 July 2021

## Problem

In quadrilateral , diagonal bisects both and . If and , find the perimeter of .

## Solution

Notice that since bisects a pair of opposite angles in quadrilateral , we can distinguish this quadrilateral as a kite.

With this information, we have that and .

Therefore, the perimeter is

~Apple321