In the given figure, if AB = 10 cm, CD = 7 cm, SD = 4 cm and AS = 5 cm, then BC = ?

Given, AB = 10 cm, CD = 7 cm, SD = 4 cm and AS = 5 cm

AP and AS are tangents to the circle from point A.

$$\Rightarrow$$  AP = AS

$$\Rightarrow$$  AP = AS = 5 cm

DR and SD are tangents to the circle from point D.

$$\Rightarrow$$  DR = SD

$$\Rightarrow$$  DR = SD = 4 cm

AB = 10 cm

$$\Rightarrow$$  AP + BP = 10

$$\Rightarrow$$  5 + BP = 10

$$\Rightarrow$$  BP = 5 cm

CD = 7 cm

$$\Rightarrow$$  DR + CR = 7

$$\Rightarrow$$  4 + CR = 7

$$\Rightarrow$$  CR = 3 cm

BP and BQ are tangents to the circle from point B.

$$\Rightarrow$$  BP = BQ

$$\Rightarrow$$  BP = BQ = 5 cm

CQ and CR are tangents to the circle from point C.

$$\Rightarrow$$  CQ = CR

$$\Rightarrow$$  CQ = CR = 3 cm

$$\therefore\ $$BC = BQ + CQ = 5 + 3 = 8 cm

Hence, the correct answer is Option D