A quadrilateral DEFG is drawn to circumscribe a circle PQRS . Find the perimeter of DEFG if PF=7cm,GQ=5cm,DR=4cm,ES=5cm.
Given, Quadrilateral DEFG circumscribes the circle PQRS.
EF, GF, GD and DE are tangents to the circle PQRS at P, Q, R and S respectively.
We know that, the lengths of tangents drawn from an external point to a circle are equal.
∴ PF = QF = 7 cm
RG = GQ = 5 cm
DS = DR = 4 cm
EP = SE = 5 cm
Perimeter of quadrilateral DEFG
= DE + EF + FG + GD
= (DS + SE) + (EP + PF) + (FQ + QG) + (GR + DR)
= (4 cm + 5 cm) + (5 cm + 7 cm) + (7 cm + 5 cm) + (5 cm + 4 cm)
= 9 cm + 12 cm + 12 cm + 9 cm
= 42 cm