A ABC is right angled at A. The sides AB, BC and
AC are the tangents to the circle with Centre 'O' as
shown in the figure. If AB = 6 cm, BC = 8 cm, find
the area of the shaded region.
Answers
Step-by-step explanation:
AB=6cm AC=8 cm
area of the triangle
1/2×6×8
24
1/2×r×24=24
r=2
area of the circle
pye r2
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Answer: 11.5 cm²
Step-by-step explanation:
We know that the length of tangents are equal.
So, length of tangents from A = x
B = y
C = z
Therefore, AB = x+y, AC = x+z, BC = y+z
We know that the centre of a circle subtends 90° on the tangent.
Therefore, we get a square by doing so with tangents from A, we get radius=x.
solving equations with x,y,z;
we have x+y = 6
x+z = 8
y+z = 10 (from pythagoras theorem)
x = 2 cm
Area of whole triangle = 1/2 bh =1/2 * 6 * 8 = 24 cm²
Area of circle= π r² = 22/7 * 4 = 88/7 cm² = 12.5 cm²
Area of shaded region = (24-12.5) cm² = 11.5 cm²