### Question 11

SSC-CGL 2020 Mar 3 Shift 2

A circle is inscribed in a quadrilateral as shown. If AB = 7 cm, BC = 6 cm and CD = 8 cm, then the length of AD is?

### Solution in Brief

By geometry, AB + DC = AD + BC, which gives AD = 9 cm ans!

### Solution in Detail

Remember: Tangents to a circle from an external point are equalLet $\displaystyle AS = x, SD = y$

[1] $\displaystyle BQ = BP = 7 - x$

[2] $\displaystyle QC = CR = 8 - y$

But $\displaystyle BQ + QC = 6$

$\displaystyle \therefore (7 - x) + (8 - y) = 6$

$\displaystyle \implies x + y = 9$

$\displaystyle \therefore AD = x + y = 9\:\underline{Ans}$

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