Letting s be the semiperimeter s=(a+b+c)/2, which is the given value of rc.
The formula for the radius of the excircle to side c is
rc = sqrt(s(s-a)(s-b)/(s-c))
Substituting the given value.
s = sqrt(s(s-a)(s-b)/(s-c))
sqrt(s(s-c))=sqrt((s-a)(s-b))
sqrt(s(s-b)(s-c)/(s-a))=s-b
This is the radius of excircle to side a.
=(a+b+c)/2 - b
=(a-b+c)/2
As required.
|
|
Posted by Jer
on 2021-03-13 08:09:00 |
Solution