1. The equation to the side BC of triangle ABC is
x + 5 = 0. If (-3,2) is the orthocentre and
(0,0) is the circumcentre then radius of the
circle is
Answers
Answer:
Step-by-step explanation:
The orthocentre, centroid, and circumcentre are collinear, because they all lie on the Euler line. The centroid divides the line segment from orthocentre to circumcentre by the ratio of 2:1. When we dilate the orthocentre with regards to the circumcentre by scale factor 1/3. The image is the centroid itself.
centroid(-1, 2/3)
Line BC is given. Call this line s. The centroid divides all medians by the of ratio 2:1, being twice as far from each vertex as it is from the opposite midpoint. When we dilate line s with respect to the centroid by factor -2. This is the image we get.
s': x = 7
Vertex A must be located on this line. The altitude from A must run through the orthocentre, perpendicular to line s. Point A also ought to lie on this line, labeled p below.
p (altitude from A): y = 2
We get A(7, 2).
The circumradius is the distance from the circumcentre to point A.
circumradius = √(7² + 2²) = √(53)
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Answer:
The equation to the side BC of is. If (—3, 2) is the orthocenter and (0, 0) is the circumcentre then radius of the circle is