The lengths of three consecutive sides of a quadrilateral circumscribing a circle are $ 4 \mathrm{~cm}, 5 \mathrm{~cm} $, and $ 7 \mathrm{~cm} $ respectively. Determine the length of the fourth side.
Given:
The lengths of three consecutive sides of a quadrilateral circumscribing a circle are \( 4 \mathrm{~cm}, 5 \mathrm{~cm} \), and \( 7 \mathrm{~cm} \) respectively.
To do:
We have to determine the length of the fourth side.
Solution:
In quadrilateral $ABCD$,
Let $BC = 4\ cm, CD = 5\ cm$ and $DA = 7\ cm$
We know that,
If a quadrilateral is circumscribed in a circle, then
$AB + CD = AD + BC$
$AB + 5 = 4 + 7$
$AB + 5 = 11$
$AB = 11 - 5 = 6$
$AB = 6\ cm$
The length of the fourth side is 6 cm.
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