(a) In figure (i) given below, triangle ABC is circumscribed, find x.
(b) In figure (ii) given below, quadrilateral ABCD is circumscribed, find x.
Solution:
(a) From A, AP and AQ are the tangents to the circle
∴ AQ = AP = 4cm
But AC =12 cm
CQ = 12 – 4 = 8 cm.
From B, BP and BR are the tangents to the circle
BR = BP = 6 cm.
Similarly, from C,
CQ and CR the tangents
CR = CQ = 8 cm
x = BC = BR + CR = 6 cm + 8 cm = 14 cm
(b) From C, CR and CS are the tangents to the circle.
CS = CR = 3 cm.
But BC = 7 cm.
BS = BC – CS = 7 – 3 =4 cm.
Now from B,BP and BS are the tangents to the circle.
BP = BS = 4 cm
From A, AP and AQ are the tangents to the circle.
AP = AQ = 5cm
x = AB = AP + BP = 5 + 4
= 9 cm