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

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.