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In Fig. Δ ABC is circumscribing a circle. Find the length of BC.

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Given:

AR = 4 cm 

BR = 3 cm 

AC = 11 cm

Property: If two tangents are drawn to a circle from one external point, then their tangent segments (lines joining the external point and the points of tangency on circle) are equal.

Using the above property, 

AR = AQ = 4 cm (tangent from A) 

BR= BP (tangent from B) 

And, 

CP = CQ (tangent from C) 

Also, 

CQ = CA – AQ = 11 cm – 4 cm = 7 cm 

Now, 

BC = BP + PC 

= BR + CQ [∵ BR = BP and CP = CQ = 7 cm] 

= 3 cm + 7 cm 

= 10 cm 

Hence, BC = 10 cm

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