SOLUTION: What are the keysteps to prove the following geometry problem?
FIND THE RADIUS OF THE CIRCLE INSCRIBED IN THE TRIANGLE ABC.
GIVEN: AC=BC=12 AB=8
Question 148: What are the keysteps to prove the following geometry problem?
FIND THE RADIUS OF THE CIRCLE INSCRIBED IN THE TRIANGLE ABC.
GIVEN: AC=BC=12 AB=8 Found 2 solutions by ichudov, rfadrogane:Answer by ichudov(507) (Show Source):
You can put this solution on YOUR website! The way I would do it is this. Draw the triangle using side AB as a horizontal base. Draw a vertical line from the middle of AB to point C. Now, consider a point that is at height X and is located on that vertical line. Distance from X to the bottom is X. Distance from X to side AC or BC can be expressed by a simple formula (find it out). The point X where these two distances are equal, would be the center of the inscribed circle, and also its radius. Good luck.
You can put this solution on YOUR website! The radius of the circle inscribed can be calculated by the formula r = A/s
where: A - area of the triangle that be solve by Hero's formula
s - the semi-perimeter (a+b+c)/2
a,b & c are the sides of the triangle.
so, by calculation: s = (12+12+8)/2 = 16
A = sq.rt.[s(s-a)(s-b)(s-c)]
= sq. rt.[16(16-12)(16-12)(16-8)]
= 45.255 unit square
thus,
r = 45.255/16
r = 2.83 unit -- answer
