1
Angle at centre = 2 × angle at circumference on the same arc
2
Angles subtended by the same chord in the same segment are equal.
3
Angle in a semicircle = 90°
FORMULA CHAPTER
Chapter 07 – Theorems Related to Angles in a Circle
WBBSEClass 10Mathematics3 formulas
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Central Angle and Inscribed Angle
Angle at centre = 2 × angle at circumference on the same arc
SymbolMeaningUnit
xangle at circumference°
yangle at centre°
Worked example
Given: angle at circumference = 35° Calculation: central angle = 2×35° Answer: 70°.
Angles in the Same Segment
Angles subtended by the same chord in the same segment are equal.
SymbolMeaningUnit
∠APB, ∠AQBangles on chord AB°
Worked example
Given: ∠APB = 48° and P,Q lie in the same segment on chord AB Calculation: ∠AQB = ∠APB Answer: ∠AQB = 48°.
Angle in a Semicircle
Angle in a semicircle = 90°
SymbolMeaningUnit
∠ACBangle subtended by diameter AB°
Worked example
Given: AB is a diameter and C lies on the circle Calculation: ∠ACB = 90° Answer: Triangle ACB is right-angled at C.