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Introduction |
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Recall that if two straight lines are not parallel, they meet at a point when produced. |
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Concurrent Line Segments Associated with a Triangle |
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Recall a line segment joining the vertex to the mid-point of the opposite side of a triangle. |
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Concurrency of the Angle Bisectors of Angles of a Triangle |
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Draw a triangle ABC. Draw its angle bisectors. The angle bisectors of a triangle are concurrent. |
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Concurrency of the Angle Bisectors of a Triangle |
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Draw a triangle ABC. Draw its angle bisectors. The angle bisectors pass through a point. |
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Concurrency of the Perpendicular Bisectors of the Sides of a Triangle |
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Draw a triangle ABC. Draw the perpendicular bisectors of its sides. The perpendicular bisectors of the sides of a triangle are concurrent (pass through the same point). |
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Theorem1 |
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To determine the incentre of a triangle, it is just sufficient to find the point of intersection of its two angles. The third angle bisector is bound to pass through it by virtue of the below theorem. |
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Theorem2 |
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To determine the circumcentre of a triangle, it is just sufficient to find the point of intersection of any two perpendicular bisectors of the sides of a triangle.> |
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Theorem3 |
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To locate orthocentre it is sufficient to draw altitudes of any two sides of a triangle. The third altitude will then automatically pass through it. |
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Theorem4 |
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The medians of a triangle pass through the same point which divides each of the medians in the ratio 2:1. |
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Summary |
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Concurrent Lines : Three or more lines are said to be concurrent if they all pass through the same point. The common point is called the point of concurrency. |
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Questions and Answers |
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