find the area of the largest triangle that can be inscribed in a semicircle of radius 21cm.
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Any triangle inscribed in a semicircle is a right angled triangle with the hypotenuse as the diameter.
 
The largest triangle that can be inscribed in the semicircle is an isosceles right triangle
​ with its right angled vertex just above the centre of the semicircle, i.e. the the line joining the right vertex and the centre should be perpendicular to the diameter.

let us suppose this triangle as triangle ABC in a circle with centre O with BC as diameter = 2 x 21 cm = 42cm 

Clearly, A is the right angled vertex and AO   |   BC .

Also AO = radius  = 21cm

thus area of triangle ABC = 1/2 x BC x AO

                                         =  1/2 x 42 x 21

                                        =  21 x 21

                                        = 441 cm2      (Ans.)








 

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