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In a circle with centre O, AB is a chord, and AP is a tangent to the circle. If ∠AOB = 140°, then the measure of ∠PAB is (SSC CGL 1st Sit. 2014)
- a)35°
- b)55°
- c)70°
- d)75°
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
In a circle with centre O, AB is a chord, and AP is a tangent to the c...
In a circle with center O, AB is a chord, and AP is a tangent to the circle. If AB = 10 cm, AP = 6 cm, and OP = 8 cm, find the radius of the circle.
Let's call the radius of the circle r.
Since AP is a tangent to the circle, the radius and the tangent are perpendicular at the point of tangency. Therefore, triangle OPA is a right triangle.
Using the Pythagorean theorem, we can find the length of OA:
OA^2 = OP^2 - AP^2
OA^2 = 8^2 - 6^2
OA^2 = 64 - 36
OA^2 = 28
OA = √28
OA = 2√7 cm
Since OA is the radius of the circle, we have r = 2√7 cm.
Let's call the radius of the circle r.
Since AP is a tangent to the circle, the radius and the tangent are perpendicular at the point of tangency. Therefore, triangle OPA is a right triangle.
Using the Pythagorean theorem, we can find the length of OA:
OA^2 = OP^2 - AP^2
OA^2 = 8^2 - 6^2
OA^2 = 64 - 36
OA^2 = 28
OA = √28
OA = 2√7 cm
Since OA is the radius of the circle, we have r = 2√7 cm.
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Community Answer
In a circle with centre O, AB is a chord, and AP is a tangent to the c...
In ΔAOB, ∠A + ∠B + ∠O = 180°
∠A + ∠B = 180 – 140° = 40°
∠A = ∠B = 20° {∵ AO = BO = radius}
∴ ∠PAO = 90° {As PA is tangent to the circle}
⇒ ∠PAB + ∠BAO = 90°
∠PAB = 90° – 20° = 70°
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In a circle with centre O, AB is a chord, and AP is a tangent to the circle. If ∠AOB = 140°, then the measure of ∠PAB is (SSC CGL 1st Sit. 2014)a)35°b)55°c)70°d)75°Correct answer is option 'C'. Can you explain this answer?
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