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.
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
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