Q) With vertices A, B and C of Δ ABC as centres, arcs are drawn with radii 14 cm and the three portions of the triangle so obtained are removed. Find the total area removed from the triangle.

From an external point P, two tangents, PA and PB are drawn  CBSE 10th board Sample paper 2023 Important questions


We know that the area made by an arc of θ angle is given by = \pi (\frac{\theta}{360}) r2

Therefore total area removed by 3 arcs at 3 vertices:

= \pi (\frac{A}{360}) r2   + \pi (\frac{B}{360}) r+ \pi (\frac{C}{360}) r

= \pi (\frac{A + B + C}{360}) r2

Since sum of all angles of a triangle is 1800, therefore ∠ A + ∠ B + ∠ C = 180

Hence, total area removed by 3 arcs at 3 vertices = \pi (\frac{180}{360}) r2

= \frac{22}{7} (\frac{1}{2}) (14)2

= 308 cm2

Therefore, the area removed from triangle is 308 cm2.

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