**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**