Question

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.

Answer 1

Given:

$AB=7cm,BC=5cm,CD=4cm$

Length of tangents drawn from an external point to the circle is equal.

$AB=a+b,BC=b+d,CD=c+d,AD=a+c$

Therefore,

$AB+CD=BC+AD=(a+b+c+d)$

Now, according to question,

$\Rightarrow 7+4=5+AD$

$\Rightarrow AD=11-5$

$\Rightarrow AD=6cm$