The lengths of three concesutive sides of a quadrilateral circumscribing a circle are 4 cm, 5 cm and 7 cm respectively. Determine the length of the fourth sides.

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Solution

Given:
$A B = 7 c m, B C = 5 c m, C D = 4 c m$
Length of tangents drawn from an external point to the circle is equal.
$A B = a + b, B C = b + d, C D = c + d, A D = a + c$

Therefore,
$A B + C D = B C + A D = (a + b + c + d)$
Now, according to question,
$\Rightarrow 7 + 4 = 5 + A D$
$\Rightarrow A D = 11 - 5$

$\Rightarrow A D = 6 c m$

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The lengths of three concesutive sides of a quadrilateral circumscribing a circle are 4 cm, 5 cm and 7 cm respectively. Determine the length of the fourth sides.

Given:AB=7 cm,BC=5 cm,CD=4 cmLength of tangents drawn from an external point to the circle is equal.AB=a+b,BC=b+d,CD=c+d,AD=a+cTherefore,AB+CD=BC+AD=(a+b+c+d)Now, according to question, ⇒7+4=5+AD⇒AD=11−5 ⇒AD=6 cm