In the quadrilateral DEFG a circle is inscribed touching quadrilateral at R, S, P, Q. If ES = 5 cm, PF = 7 cm, QG = 5 cm, DR = 4 cm; then perimeter of the quadrilateral is …………
(A) 40 cm
(B) 21 cm
(C) 42 cm
(D) 20 cm
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Correct option is (C) 42 cm
\(\because\) Tangents from an outer point to a circle are of equal length.
\(\therefore ER=ES=5\,cm,\) (Tangents of circle from point E & ES = 5 cm)
\(SF=PF=7\,cm,\) (Tangents of circle from point F & PF = 7 cm)
\(GP=QG=5\,cm\) (Tangents of circle from point G & QG = 5 cm)
and \(QD=DR=4\,cm\) (Tangents of circle from point D & DR = 4 cm)
\(\therefore\) Perimeter of quadrilateral DEFG
\(=(DR+ER)+(ES+SF)\) \(+(PF+GP)+(QG+QD)\)
\(=(4+5)+(5+7)+(7+5)+(5+4)\)
\(=9+12+12+9\)
\(=18+24=42\,cm\)
Correct option is: (C) 42 cm