Properties Of Circle
In this topic, you will learn the key properties of a circle and how to apply them to solve geometry problems effectively. You will explore important angle properties, especially those involving triangles and quadrilaterals formed within the circle.
To help students better identify the properties, the concept is divided into 4 categories:
- Tangents & Isosceles Triangle
- Triangles Inside The Circle
- Quadrilateral Inside The Circle
- Two Tangents To A Circle
Related Lessons:
Tangent & Isosceles Triangle
For the property Radius ⊥Tangent:
- Line AC touches the circle at a single point X, i.e. tangent to the circle
- Line OX is the radius of the circle
- Angle AXO is 90°
For the property isosceles triangle inside the circle
- Line OA & OB are radius of the circle centre O
- Triangle OAB is isosceles
- Angle OAB = Angle OBA
Triangles Inside The Circle
For the property Angle In Semicircle:
- AC is the diameter
- A, B and C touches the circumference
- Angle ABC is 90°
For the property Angle In The Same Segment
- A, B, C and D touches the circumference
- Two triangles ABC and ADC share a common base, line AC
- Angle ABC = Angle ADC
For the property Angle At Centre = 2 × Angle At Circumference:
- A, B, C touches the circumference, and O is the centre of the circle
- Two triangles ABC and AOC share a common base, line AC
- Angle AOC = 2 x Angle ABC
Quadrilateral Inside The Circle
For the property Opposite Angle Of Cyclic Quad:
- A, B, C and D touches the circumference
- ABCD is a quadrilateral
- ∠DAC+∠DBC=180º
- ∠ADB+∠ACB=180º
For the property Angle In Opposite Segment:
- A, B, C touches the circumference.
- O is the centre of the circle.
- ABCO is a quadrilateral
- Reflex Angle AOC = 2 x Angle ABC
Two Tangents To A Circle
For the property Tangent From External Point:
- Two lines, XA and XB are tangent to the circle at A and B respectively
- OA and OB are radius to the circle centre O
- Angle BXO = Angle AXO
- Angle BOX = Angle AOX
- AX = BX