Circles ncert solutions Chapter 10 Exercise 10.2 Question 12
12. A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively. Find the sides AB and AC.
Solution:
It is given that CD=6 cm and BD = 8 cm.
And Radius of circle = OD=OF=OE=4cm
Two tangents drawn from an external point to the circle are equal.
Therefore, CD=CE=6 cm And, BD=BF=8cm
Let AE =AF= x cm
We can find area of triangle using Heron’s formula:
Semi-perimeter(s) =
cm
Area of Triangle =
Area of Triangle
(1)
Also, Area of
= Area of
+ Area of
+ Area of
(2)
From (1) and (2), we can say that
Squaring both sides, we get
We discard x =-14 because length cannot be in negative.
Therefore, x=7 cm
It means
cm
cm
Prashant Gupta says
Do you know any new method for solving this ques.