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
cm2
B. 40 – 12
cm2
C. 40 – 15
cm2
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 + x2 – 100 – 20x – x2
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 cm2
Radius of in-circle = =
= 2
Area of In-circle = = 12
Hence, required area = Area of ΔABC – Area of In-circle
= 40 – 12
cm2
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A circle is inscribed in a triangle ABC. It touches side AB at point X