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AB 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).
- a)31º
- b)62º
- c)28º
- d)66º
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
AB is a diameter of a circle with center O. A tangent is drawn at poin...
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°
Most Upvoted Answer
AB is a diameter of a circle with center O. A tangent is drawn at poin...
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°
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Community Answer
AB is a diameter of a circle with center O. A tangent is drawn at poin...
We let θ be the angle between the tangent line and the line segment OC, then the angle between the tangent line and the line segment AB is also θ, since AB is a diameter and OC is a radius.
Since AB is a diameter, the angle at point C is a right angle. Therefore, the angle at point P is also a right angle, since the tangent line is perpendicular to the radius at the point of tangency.
Since the angle at point B is a right angle, the angle at point P is also a right angle, since BC produced meets the tangent line at point P.
Therefore, the angles at points C and P are both right angles, and the angle at point A is θ.
Since AB is a diameter, the angle at point C is a right angle. Therefore, the angle at point P is also a right angle, since the tangent line is perpendicular to the radius at the point of tangency.
Since the angle at point B is a right angle, the angle at point P is also a right angle, since BC produced meets the tangent line at point P.
Therefore, the angles at points C and P are both right angles, and the angle at point A is θ.
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AB 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).a)31ºb)62ºc)28ºd)66ºe)None of theseCorrect answer is option 'C'. Can you explain this answer? for UCAT 2025 is part of UCAT preparation. The Question and answers have been prepared according to the UCAT exam syllabus. Information about AB 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).a)31ºb)62ºc)28ºd)66ºe)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for UCAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for AB 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).a)31ºb)62ºc)28ºd)66ºe)None of theseCorrect answer is option 'C'. Can you explain this answer?.
AB 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).a)31ºb)62ºc)28ºd)66ºe)None of theseCorrect answer is option 'C'. Can you explain this answer? for UCAT 2025 is part of UCAT preparation. The Question and answers have been prepared according to the UCAT exam syllabus. Information about AB 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).a)31ºb)62ºc)28ºd)66ºe)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for UCAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for AB 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).a)31ºb)62ºc)28ºd)66ºe)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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