Question
In Fig., the sides AB, BC and CA of a triangle ABC, touch a circle at P, Q and R respectively. If PA = 4 cm, BP = 3 cm and AC = 11 cm, then the length of BC (in cm) is
11
10
14
15
Solution
B.
10
it is know that the lengths of tangents drwan from a point outside a circle
are equal in length.
Therefore, we have;
AP = AR ........(1) (Tangents drawn from point A)
BP = BQ .........(2) (Tangents drawn from point B)
CQ = CR ..........(3) (Tangents drawn from point C)
Using the above equations,
AR = 4 cm ( AP = 4 cm, given)
BQ = 3 cm ( BP = 3 cm, given)
AC = 11 cm RC = 11 cm - 4 cm = 7 cm
Hence, BC = BQ + CQ = 3 CM + 7 CM = 10 cm.
