Unit 5 · Class 10 IB MYP · Formula Sheet
Circle Theorems Formulas — Class 10 IB MYP
Prove and apply circle theorems including angle in a semicircle, cyclic quadrilaterals, and tangents.
Key Formulas
Angle at Centre
2 \times \text{Angle at circumference}
Angle in Semicircle
90°
Same Segment
\text{Angles in same segment are equal}
Cyclic Quadrilateral
\text{Opposite angles sum to } 180°
Tangent-Radius
\perp
Alternate Segment
\text{Angle between tangent and chord} = \text{angle in alternate segment}
Worked Examples
1Using: Area of Circle
Find the area of a circle with radius 7 cm.
Step 1: Area = pi x r^2
Step 2: = 22/7 x 49 = 154 sq. cm.
Answer: 154 sq. cm
2Using: Circumference
Find the circumference of a circle with radius 14 cm.
Step 1: C = 2 x pi x r
Step 2: = 2 x 22/7 x 14 = 88 cm.
Answer: 88 cm
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