Question

The four sides of a quadrilateral ABCD are tangential to a circle. If AB =7.2cm, BC =8.5cm, and DA =6.9cm, then CD =?

Answer 1

Answer:

DC=8.2

Step-by-step explanation:

1. AP=AS
2. BP=BQ
3. CR=CQ
4. DR=DS

FROM 1. 2. 3. 4.

BY ADDING

AP+BP+CR+DR=CQ+BQ+AS+DS

AB + DC = CB+AD

7.2+DC = 8.5+6.9

7.2+DC = 15.4

DC=15.4—7.2

DC=8.2

Answer 2

The length of the fourth side = 8.2 cm.

Let ABCD be a quadrilateral with sides AB = 7.2 cm, BC = 8.5 cm, DA = 6.9 cm and CD = x circumscribing a circle at points E, F, G and H.

Consider the figure, while going through the following steps.

As the tangents drawn from an external point to the same circle are of equal length, we have,

AE = AH

BE = BF

CG = CE

DG = DH

Adding above all the equations, we have,

AE + BE + CG + DG = AH + BF + CE + DH

AB + CD  = AD + BC

7.2 + x = 6.9 + 8.5

7.2 + x = 15.4

x = 15.4 -  7.2

x = 8.2 cm

CD =  8.2 cm.

The length of the fourth side = 8.2 cm.