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SIMILAR TRIANGLES : Geometry is the right foundation of all painting, I have decided to teach its rudiments and principles to all youngsters eager for art. (Ans: r=2)
Example
ABC is a right-angled triangle, right-angled at A. A circle is inscribed in it. The lengths of the two sides containing the right angle are 6cm and 8 cm. Find the radius of the in circle.
Ans: BC = 10cm
y + z = 8cm
x + z = 6cm
x + y = 10
⇒ x + y + z = 12
z = 12 - 10
z = 2 cm
∴radius = 2cm
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Taking 2^x=m and solving the quadratic for getting D>=0 we get range= [3/4 , infinity )
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if the sum of lengths of hypotenuse and a side of right triangle are given, prove the area of the triangle is maximum when angle between them is pi/3
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whta are the formulas needed for proving in trignometry .
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