Answer:
Part A: The center of The inscribed circle is the point S
Part B: The center of The circumscribed circle is the point P
Step-by-step explanation:
Part A: Find the center of The inscribed circle of ΔABC
The inscribed circle will touch each of the three sides of the triangle in exactly one point,
The center of the inscribed circle is the point of intersection between the angle bisectors of the triangle.
<u>So, </u>According to the previous definition:
A₁A₂ and B₁B₂ are the angle bisectors of ∠A and ∠B
So, the inter section between them is the center of <u>The inscribed circle</u>
<u>So, the center of The inscribed circle is the point S</u>
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Part B: Find the center of The circumscribed circle of ΔABC
The circumscribed circle is the circle that passes through all three vertices of the triangle.
The center of the circumscribed circle is the point of intersection between the perpendicular bisectors of the sides.
<u>So,</u> According to the previous definition:
P₁P₂ and Q₁Q₂ are the perpendicular bisectors of AB and BC
So, the inter section between them is the center of <u>The circumscribed circle</u>
<u>So, the center of The circumscribed circle is the point P</u>
