Question

5. A circle is inscribed in a square. An equilateral triangle of side 4/3 cm is inscribed in that cirele. The length
of the diagonal of the square is
(b) 8 cm
(c) 8/2 cm (d) 16 cm
.please solve fast​

Answer 1

Answer:

that is actually 4√3 cm

Step-by-step explanation:

As given in the question, in the figure above, a circle is inscribed in a square and an equilateral triangle is inscribed in a circle. Let the centre of circle is O, drop a perpendicular line OA to a side of equilateral triangle and join the centre O to the vertex B of equilateral triangle as shown in figure. A triangle OAB is formed. It can be seen from figure this ΔOAB has angles 30°, 60° and 90°. Hence sides are in the ratio 1:√3:2 . Side opposite to 90° is twice the side opposite to 30° . Side AB = 2√3 cm ( half of the side of equilateral triangle) . Hence OA = 2 cm and OB = 4 cm. Hence circle diameter = side of square = 8 cm Hence diagonal of square 8√2 cm

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