Ex 7.5, 3 (Optional)
In a huge park, people are concentrated at three points (see Fig. 7.52):
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 ice-cream parlour be set up so that maximum number of persons can approach it?
(Hint : The parlour should be equidistant from A, B and C)
The ice-cream parlour should be equidistant from points A, B and C
An interior point which is equidistant from all the vertices of ∆ABC is its circumcentre
Let’s join A, B and C
And draw a circle passing through points A, B, C
So,
Center of a circle will be equidistant from points A, B, C
Center of circle will be the intersection of
perpendicular bisector of sides of the triangle.
Because perpendicular bisector of a chord passes through the center.
Finding center of circle
Draw perpendicular bisector of AB Take a compass. With point A as pointy end and B as pencil end of the compass, mark an arc above and below AB. Do same with B as pointy end and A as pencil end of compass.
Mark point O where two perpendicular bisectors intersect
Hence, O is the center of the circle
Thus, point O is the point where the ice-cream stand should be placed

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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