Ex - 7.5
Question 1. ABC is a triangle. Locate a point in the interior of
ABC which is equidistant from all the vertices of ABC.
Solution
Circumcentre of a triangle is always equidistant from all the vertices of that triangle. Circumcentre is the point where perpendicular bisectors, of all the sides of triangles meet together.
As here inABC we can find the circumcentre by drawing the perpendicular bisectors of sides AB, BC, and CA of this triangle. O is the point where these bisectors are meeting together. So O is point which is equidistant from all the vertices of ABC.
Question 2. In a triangle locate a point in its interior which is equidistant from all the sides of the triangle.
Solution
The point which is equidistant from all the sides of a triangle is incenter of triangle. Incentre of triangle is the intersection point of angle bisectors of interior angles of that triangle.
Here in
ABC we can find the incentre of this triangle by drawing the angle bisectors of interior angles of this triangle. I is the point where these angle bisectors are intersecting each other. So, I is the point, equidistant from all the sides of ABC.
Question 3. In a huge park people are concentrated at three points (see the given figure)
A: where there 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 exit.
Where should an icecream parlour be set up so that maximum number of persons can approach it?
(Hint: The parlor should be equidistant from A, B and C)
Solution
Ice-cream parlour should be set up at the circumcentre O of
ABC.
In this situation maximum number of persons can approach to it. We can find circumcentre O of this triangle by drawing perpendicular bisectors of the sides of this triangle.
Question 4. Complete the hexagonal and star shaped Rangolies (see the given figures) by filling them with as many equilateral triangles of side 1 cm as you can. Count the number of triangles in each case. Which has more triangles?
Solution
We may observe that hexagonal shaped rangoly is having 6 equilateral triangles in it.
Question 1. ABC is a triangle. Locate a point in the interior of
ABC which is equidistant from all the vertices of ABC.Solution
Circumcentre of a triangle is always equidistant from all the vertices of that triangle. Circumcentre is the point where perpendicular bisectors, of all the sides of triangles meet together.
As here in
ABC we can find the circumcentre by drawing the perpendicular bisectors of sides AB, BC, and CA of this triangle. O is the point where these bisectors are meeting together. So O is point which is equidistant from all the vertices of ABC.Question 2. In a triangle locate a point in its interior which is equidistant from all the sides of the triangle.
Solution
The point which is equidistant from all the sides of a triangle is incenter of triangle. Incentre of triangle is the intersection point of angle bisectors of interior angles of that triangle.
Here in
ABC we can find the incentre of this triangle by drawing the angle bisectors of interior angles of this triangle. I is the point where these angle bisectors are intersecting each other. So, I is the point, equidistant from all the sides of ABC.Question 3. In a huge park people are concentrated at three points (see the given figure)
A: where there 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 exit.
Where should an icecream parlour be set up so that maximum number of persons can approach it?
(Hint: The parlor should be equidistant from A, B and C)
Solution
Ice-cream parlour should be set up at the circumcentre O of
ABC.In this situation maximum number of persons can approach to it. We can find circumcentre O of this triangle by drawing perpendicular bisectors of the sides of this triangle.
Question 4. Complete the hexagonal and star shaped Rangolies (see the given figures) by filling them with as many equilateral triangles of side 1 cm as you can. Count the number of triangles in each case. Which has more triangles?
Solution
We may observe that hexagonal shaped rangoly is having 6 equilateral triangles in it.
Area of 
OAB = 
(side)2 = (5)2
OAB = (side)2 = (5)2
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