Question
Download Solution PDFAB is a diameter of a circle with center O. A tangent is drawn at point A. C is a point on the circle such that BC produced meets the tangent at P. If ∠APC = 62º, then find the measure of the minor arc AC(i.e.∠ ABC).
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
AB is a diameter of a circle with a center O
∠APC = 62º
Concept used:
The radius/diameter of a circle is always perpendicular to the tangent line.
Sum of all three angles of a triangle = 180°
Calculation:
Minor arc AC will create angle CBA
∠APC = 62º = ∠APB
∠BAP = 90° (diameter perpendicular to tangent)
In Δ APB,
∠APB + ∠BAP + ∠PBA = 180°
⇒ ∠PBA = 180° - (90° + 62°)
⇒ ∠PBA = 28°
∴ The measure of minor arc AC is 28°
Mistake PointsMeasure of the minor arc AC is asked,
∠ABC marks arc AC,
∴ ∠ABC is the correct angle to show a measure of arc AC
This is a previous year's question, and according to the commission, this is the correct answer.
Last updated on Jun 10, 2025
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