The figure shows a circle circumscribed around a triangle.

Triangle U T V is inscribed within a circle. A point is at the center of the triangle. Lines are drawn from the points of the triangle to the point in the middle. Lines are drawn from the point in the middle to the sides of the triangle to form right angles.

What is constructed first when creating the circle?
perpendicular segments to the vertices of the triangle
perpendicular bisectors of the sides of the triangle
angle bisectors of each angle of the triangle
the incenter of the triangle

Question

07-07-2022
Mathematics

Answered

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The figure shows a circle circumscribed around a triangle.

Triangle U T V is inscribed within a circle. A point is at the center of the triangle. Lines are drawn from the points of the triangle to the point in the middle. Lines are drawn from the point in the middle to the sides of the triangle to form right angles.

What is constructed first when creating the circle?
perpendicular segments to the vertices of the triangle
perpendicular bisectors of the sides of the triangle
angle bisectors of each angle of the triangle
the incenter of the triangle

Sagot :

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shubhamchouhanvrVT shubhamchouhanvrVT · Answer 1 · 2022-07-09T02:42:57-04:00

Option B is right perpendicular bisectors of the sides of the triangle

What circumcircle?

If we draw a circle through all the vertices of a triangle then the circle obtained is the circumcircle of the given triangle. We have in a triangle there are some properties inherent.

One is the perpendicular bisectors of all sides are concurrent. These three concur at a point called the circumcentre of the triangle.

When we draw a perpendicular bisector for a side AB, we get that all points on the perpendicular bisector are equidistant from A and B.

When we take the point of intersection of the perpendicular bisector of AB and BC, we have the intersecting point S(say) is equidistant from A and B and also from B and C

In short, this is equidistant from all 3 vertices and hence is the centre of the circumcircle of triangle ABC

Therefore Option B is right perpendicular bisectors of the sides of the triangle.

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Sagot :

What circumcircle?

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