Question
Find the incenter of triangle $\left(-7,~-13\right)$ $\left(5,~3\right)$ $\left(-7,~3\right)$.
Answer
The incenter (center of the incircle) of the triangle $ ABC $ is point:
$$ \left(-3,~-1\right) $$Explanation
explanation
The incenter of a triangle is given by:
$$ C = \left( ~ \frac{a \cdot A_x + b \cdot B_x + c \cdot C_x}{a + b + c}~,~ \frac{a \cdot A_y + b \cdot B_y + c \cdot C_y}{a + b + c} \right) $$where $ a = d(B,C)$ , $ b = d(A,C) $ and $ c = d(A,B) $.
In this example we have : $ A_x = -7 $ , $ A_y = -13 $ , $ B_x = 5 $ , $ B_y = 3 $ , $ C_x = -7 $ and $ C_y = 3 $ .
The sides lengths are: $ a = 12 $ , $ b = 16 $ and $ c = 20 $.
When we insert these values into the formula, we obtain the given result.
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