Theorems on Circles at both the Intermediate and Higher tier are difficult areas for students, which teachers often find equally difficult to deliver.Here, I have explained some Circle theorems based on circle so that student can understand them easily.

1) If two arcs of a circle are congruent, then corresponding chords are equal.

Statements |
Reasons |

1) BC = PQ | 1) Given |

2) OP = AB | 2) Radius of a circle |

3) OQ = AC | 3) Radius of a circle |

4) ΔPOQ = ΔBAC | 4) SSS Postulate |

5) ∠POQ = ∠BAC | 5) CPCTC |

Statements |
Reasons |

1) OP = OQ | 1) Radii of the same circle. |

2) OM = OM | 2) Reflexive (common) |

3) ∠OMP = ∠OMQ | 3) Each 90^{0} |

4) ΔPMO = ΔQMO | 4) HL postulate(RHS) |

5) PM = MQ | 5) CPCTC |

Statements |
Reasons |

1) AB = AC | 1) Given |

2) ∠BAM = ∠CAM | 2) Given |

3) AM = AM | 3) Reflexive (Common) |

4) ΔBAM = ΔCAM | 4) SAS Postulate |

5) BM = CM and ∠BMA = ∠CMA | 5) CPCTC |

6) ∠BMA + ∠CMA = 90^{0} |
6) Linear pair angles |

7) AM = BM and ∠BMA = ∠CMA = 90^{0} |
7) From (6) |

8) AM is the perpendicular bisector of BC | 8) Definition of perpendicular bisector. |

9) AM passes through the center O. | 9) Perpendicular bisector of a chord always passes through the center. |

• Theorems on Chord

• Theorems on Chord and Subtended Angle

• Theorems on Arc and Angle

• Theorems on Cyclic Quadrilateral

GMAT

GRE

1st Grade

2nd Grade

3rd Grade

4th Grade

5th Grade

6th Grade

7th grade math

8th grade math

9th grade math

10th grade math

11th grade math

12th grade math

Precalculus

Worksheets

Chapter wise Test

MCQ's

Math Dictionary

Graph Dictionary

Multiplicative tables

Math Teasers

NTSE

Chinese Numbers

CBSE Sample Papers