Worksheet: Constructing Circles

In this worksheet, we will practice constructing circles given one, two, or three points.

Q1:

How many circles can pass through one point?

  • A3
  • B2
  • C0
  • D1
  • EAn infinite number

Q2:

How many circles can pass through two points?

  • A1
  • BAn infinite number
  • C2
  • D3
  • E0

Q3:

How many circles can pass through three points?

Q4:

Consider the two points 𝐴 and 𝐡. What is the radius of the smallest circle that can be drawn in order to pass through the two points?

  • A12𝐴𝐡
  • B14𝐴𝐡
  • C3𝐴𝐡
  • D2𝐴𝐡
  • E𝐴𝐡

Q5:

Can we use point 𝑁 in the given shape to draw a circle that passes through the vertices of triangle 𝐴𝐡𝐢?

  • ANo
  • BYes

Q6:

True or False: If a circle passes through three points, then the three points should belong to the same straight line.

  • AFalse
  • BTrue

Q7:

True or False: Two circles can intersect at more than two points.

  • ATrue
  • BFalse

Q8:

True or False: A circle can be drawn through the vertices of any triangle.

  • ATrue
  • BFalse

Q9:

In the following figures, two types of constructions have been made on the same triangle, 𝐴𝐡𝐢. Which point will be the center of the circle that passes through the triangle’s vertices?

  • A𝐡
  • B𝑁
  • C𝐹
  • D𝐢
  • E𝐴

Q10:

In the figure, which point can be used as center of a circle that passes through the two points 𝐴 and 𝐡?

  • A𝐡
  • B𝑁
  • C𝑀
  • D𝐴
  • E𝑃

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