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A circle centered at B is tangent to AC. In triangle ABC, AB = 6, BC = 8  and CA = 12. What is the radius of this circle?

 Nov 2, 2020
 #2
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Hint:  Use Heron's formula to calculate the area, then use this formula  (h = 2*A / a) to find the radius.

 

The altitude from point B to line segment AC is the radius of a circle.

 Nov 3, 2020
 #3
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Here is another way, (though Heron's formula is probably easier.

 

Let X be the point of intersection of the circle and the tangent

Let r be the radius

 

Now you have triangles BCX  and  BAX

 

The angles at X are right angles so you can use pythagoras's theorum to find XC  and  XA  in terms of r

added they equal 12

 

solve

(it is a bit tricky)

 Nov 3, 2020

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