Question
Download Solution PDFAB is a chord of a circle with centre O. C is a point on the circumference of the circle in the minor sector. If ∠ABO = 40°, what is the measure (in degree) of ∠ACB?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
∠ABO = 40°
Concept:
The angle subtended by an arc at the center is double than subtended by it on other parts of the circle. In the figure below, ∠ AOB = 2∠ACB
Calculation:
In the figure ∠ABO = ∠BAO (angles formed by the radius are equal)
In Δ AOB, ∠ABO + ∠BAO + ∠BOA = 180°
⇒ ∠BOA = 180° - (40 + 40) = 100°
⇒ ∠BOA (external) = 360° - 100° = 260°.
∠ACB =
∴ ∠ACB =
∴ The angle formed by ∠ACB is 130°.
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