# A circle is inscribed in a triangle ABC. It touches side AB at point X

| A circle is inscribed in a triangle ABC. It touches side AB at point X. If ∠A = 60˚ AX = 6 cm, BX = 10 cm, then find the area of the region outside the circle in triangle:

A. 40 – 6 cm^{2}

B. 40 – 12 cm^{2}

C. 40 – 15 cm^{2}

D. Can’t be determined

### Right Answer is: B

#### SOLUTION

Let CY = CZ = x cm (Tangents drawn from a common point)

In ΔABC,

BX = BY & AX = AZ (Tangents drawn from a common point)

Apply the cosine rule,

Cos60˚ =

96 + 16x = 256 + 36 + 12x + x^{2} – 100 – 20x – x^{2}

96 + 16x = 192 – 8x

24x = 96

x = 4 cm

Now, side AC = 6 + x = 6 + 4 = 10 cm,

BC = 10 + x = 10 + 4 = 14 cm

Semi-perimeter of ΔABC = = 20 cm

Area of ΔABC =

=

=

= 40 cm^{2}

Radius of in-circle = = = 2

Area of In-circle = = 12

Hence, required area = Area of ΔABC – Area of In-circle

= 40 – 12 cm^{2}

Share

A circle is inscribed in a triangle ABC. It touches side AB at point X