In the quadrilateral DEFG a circle is inscribed touching quadrilateral

1.	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
Answer» 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

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

Answer»

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