Complete each of the following statements - Leaving Cert Mathematics - Question 6A - 2013
Question 6A
Complete each of the following statements.
(i) The circumcentre of a triangle is the point of intersection of ____________________________________________________
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Worked Solution & Example Answer:Complete each of the following statements - Leaving Cert Mathematics - Question 6A - 2013
Step 1
Complete the following statements (i)
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Answer
The circumcentre of a triangle is the point of intersection of the perpendicular bisectors of the sides of the triangle.
Step 2
Complete the following statements (ii)
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Answer
The incentre of a triangle is the point of intersection of the bisectors of the angles of the triangle.
Step 3
Complete the following statements (iii)
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Answer
The centroid of a triangle is the point of intersection of the medians of the triangle.
Step 4
Explain why the circumcentre, incentre, and centroid are the same in an equilateral triangle
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Answer
In an equilateral triangle, the medians are perpendicular to the opposite sides and bisect the angles. Therefore, the perpendicular bisectors of the sides, the bisectors of the angles and the median are the same line and intersect at one point.
Step 5
Construct the orthocentre of the triangle ABC below
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Answer
To construct the orthocentre, first draw the perpendiculars from each vertex (A, B, C) to the opposite side. These lines will intersect at the orthocentre.
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