an incircle is drawn touching the sides of a right angle triangle the base and the perpendicular are 6cms and 2.5 CMS respectively.find the radius of the circle
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The way to solve this is to draw a line from radius to all 3 vertices - so you have 3 separate lines. This creates OA, OB, and OC and 3 smaller triangles within the larger 6-2.5-6.5 triangle. THe sum of the 3 smaller triangles should equal the sum of the large triangle.
The reason we care about the smaller triangles is because we know their "height" is going to be "r". So 1/2 * base * height, the height will be r.
1/2 * 6* r + 1/2 * 2.5 * r + 1/2 * 6.5* r = 1/2 * 2.5* 6
1/2(6+2.5+6.5)r = 1/2*2.5*6
1/2(15)r = 1/2*15
r = 1. Ans
The reason we care about the smaller triangles is because we know their "height" is going to be "r". So 1/2 * base * height, the height will be r.
1/2 * 6* r + 1/2 * 2.5 * r + 1/2 * 6.5* r = 1/2 * 2.5* 6
1/2(6+2.5+6.5)r = 1/2*2.5*6
1/2(15)r = 1/2*15
r = 1. Ans
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