A quadrilateral DEFG is drawn to circumscribe a circle PQRS . Find the perimeter of DEFG if PF=7cm,GQ=5cm,DR=4cm,ES=5cm.

Dear Student!

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

Cheers!