Circle Theorem Game

Circle Theorem Game
In this game, you need to identify specific geometric laws based on the diagrams and descriptions provided. Scroll down the page for a more detailed explanation.
 

 

How to Play the Circle Theorem Game

1. Choosing Your Difficulty
   When you launch the game, you are presented with two modes:
   Normal Mode: Best for learning. You are given a geometric diagram and a written description of the theorem.
   Hard Mode: Purely visual. You must identify the theorem based on the lines, angles, and shapes shown in the circle diagram.
   
   
2. How to Identify the Theorems
   Angle at the Centre
   The angle subtended by an arc at the center is exactly twice the angle subtended by the same arc at the circumference.
   How to identify: Look for a “V” or “Arrowhead” shape. One point must be at the center (the dot), and the other point must be on the edge.
   The Rule: Center Angle = 2 × Edge Angle.
   
   Angle in a Semicircle
   The angle subtended by a diameter at the circumference is always 90°.
   How to identify: Look for a triangle where the longest side is a straight line going through the center (the diameter).
   The Rule: The corner opposite the diameter is always exactly 90°.
   
   Angles in the Same Segment
   Angles subtended by the same arc at the circumference are equal.
   How to identify: Look for two triangles that share the same base, forming a “Bow Tie” or “Butterfly” shape. All four corners must touch the circle’s edge.
   The Rule: The angles at the “top” of the wings are equal; the angles at the “bottom” are also equal.
   
   Cyclic Quadrilateral
   Opposite angles in a cyclic quadrilateral sum to 180°.
   How to identify: Look for any four-sided shape (quadrilateral) where every single corner touches the circle’s circumference.
   The Rule: Angle A + Angle C = 180°; Angle B + Angle D = 180°.
   
   Tangent-Radius Theorem
   A tangent to a circle is perpendicular to the radius at the point of contact.
   How to identify: Look for a T-junction: a straight line that just touches the outside of the circle (the tangent) meeting a line from the center (the radius).
   The Rule: The intersection always forms a perfect 90° angle.
   
   Tangents from a Point
   Tangents to a circle from the same external point are equal in length.
   How to identify: Look for two lines starting from the same point outside the circle and touching the circle’s edges. It often looks like an Ice Cream Cone.
   The Rule: The two tangent lines are identical in length. This often creates an isosceles triangle if you connect the two points of contact.
   
   Alternate Segment Theorem
   The angle between a tangent and a chord is equal to the angle in the alternate segment.
   How to identify: This is the “trickiest” one. Look for a triangle inside the circle where one of its corners touches a tangent line on the outside.
   The Rule: The angle between the outside tangent and the triangle’s side is the same as the angle at the far corner inside the triangle.
   
   
3. Scoring and Results
   The Score Counter at the top tracks your progress (Correct / Total played).
    
   

The video gives a clear, step-by-step approach to identify the circle theorems.

• Show Video

 

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