Hinglish

Points Equidistant from Two Points

Class 6 Maths · Chapter 8: Playing with Constructions · NCERT Ganita Prakash section 8.6

Learn

Ira and Kabir live in houses B and C, 6 km apart. They want to meet at a tea stall that is 5 km from both of them. Where could the stall be? On a map with 1 cm for 1 km, B and C are 6 cm apart.

Every point 5 cm from B lies on a circle of radius 5 cm around B. Every point 5 cm from C lies on a circle of radius 5 cm around C. The stall must be on both circles, so it is where they cross.

The circles cross at two points, one above BC and one below. Both are 5 km from Ira and from Kabir. You don't need whole circles: two short arcs near the crossing are enough.

This is how to build a tent shape (a triangle with two equal sides) on a base BC: arcs of the same radius from B and from C meet at the top. If the radius is too small (less than half of BC), the arcs never meet!

Explore: use circles to find the right points, then mark one.

  1. Mark a point that is 5 cm from B and 5 cm from C.
  2. Mark any point that is the same distance from B and from C.
  3. New points: mark a point 5 cm from both P and Q.

Remember

  • Points at the same distance from B and from C: draw equal circles (or arcs) around both; they meet at those points.
  • Equal circles around B and C meet twice, once, or never, depending on the radius.

Quick check

B and C are 10 cm apart. How many points are exactly 4 cm from both?

  1. 0
  2. 1
  3. 2
  4. 4
Answer

0. 4 + 4 = 8, which is less than 10, so the two 4 cm circles never meet.

Think about it

All the points that are the same distance from B and C lie on one line. Where is that line?

One answer

It goes straight through the middle point of BC, at right angles to BC. Every point on it is just as far from B as from C.

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.