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What can you say about BC and BD? Show that CD bisects AB. Thus, CD bisects AB. AS is a line segment and P is its mid-point. Point D is joined to point B see figure. Join A to 0. Show that these altitudes are equal. Show that in a right angled triangle, the hypotenuse is the longest side. Therefore, we get AC is the longest side. But AC is the hypotenuse of the triangle. Thus, the hypotenuse is the longest side. Solution: Let us join AC. Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
Thus, the perpendicular line segment is the shortest line segment drawn on a line from a point not on it. ABC is a triangle. Draw l, the perpendicular bisector of AB. Draw m, the perpendicular bisector of BC. Let the two perpendicular bisectors l and m meet at O.
O is the required point which is equidistant from A, B and C. The point O is called circumcentre of the triangle. In a triangle locate a point in its interior which is equidistant from all the sides of the triangle. Let the two bisectors l and m meet at O. Point O is called incentre of the triangle. In a huge park, people are concentrated at three points see figure A: where these are different slides and swings for children.
B: near which a man-made lake is situated. C: which is near to a large parking and exist. Where should an ice-cream parlor be set? Now, join B and C, and draw m, the perpendicular bisector of BC. Let the perpendicular bisectors l and m meet at O. The point O is the required point where the ice cream parlour be set up. Note: If we join A and C and draw the perpendicular bisector, then it will also meet or pass through the point O.
Complete the hexagonal and star shaped Rangolies [see Fig. Count the number of triangles in each case. Which has more triangles? Solution: It is an activity. We require equilateral triangles of side 1 cm in the Fig. RD Sharma Class 12 Solutions.
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