SOLUTION: The base of an isosceles triangle is a=24cm side b=20cm find radius r and R (circumscribed and inscribed circle)

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Question 1083153: The base of an isosceles triangle is a=24cm side b=20cm find radius r and R (circumscribed and inscribed circle)
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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For the radius of the circumscribed circle use the formula 


R = abc%2F4S,


where a, b and c are the sides measures and S is the area of the triangle.


(See the lesson  Proof of the formula for the radius of the circumscribed circle  in this site).



For the radius of the inscribed circle use the formula 


r = S%2Fp,


where a, b and c are the sides measures and p is the semi-perimeter of the triangle.


(See the lesson  Proof of the formula for the area of a triangle via the radius of the inscribed circle  and   in this site).


To find the area of the given triangle, find its altitude drawn to the base first:

h = sqrt%28b%5E2+-+%28a%2F2%29%5E2%29 = sqrt%2820%5E2+-+12%5E2%29 = sqrt%28400-144%29 = sqrt%28256%29 = 16 cm.


Then the area of the triangle is S = %281%2F2%29%2Aa%2Ah = %281%2F2%29%2A24%2A16 = 192 cm^2.

From this point, complete the solution on your own.

Also,  you have this free of charge online textbook on Geometry
    GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.

The referred lessons are the part if this textbook under the topic "Area of triangles".