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P is a point outside a circle and is 13 cm away from its centre. A secant drawn from the point P intersect the circle at points A and B in such a way that PA = 9 cm and AB = 7 cm. The radius of the circle is: (SSC CGL 2nd Sit. 2012)
- a)5.5 cm
- b)5 cm
- c)4 cm
- d)4.5 cm
Correct answer is option 'B'. Can you explain this answer?
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P is a point outside a circle and is 13 cm away from its centre. A sec...
OC ⊥ AB
AC = BC = 3.5 cm OP = 13 cm
PC = 9 + 3.5 = 12.5 cm
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P is a point outside a circle and is 13 cm away from its centre. A sec...
Given:
- Point P is outside the circle.
- Distance between point P and the center of the circle is 13 cm.
- A secant drawn from point P intersects the circle at points A and B.
- PA = 9 cm and AB = 7 cm.
To find: The radius of the circle.
Solution:
Let O be the center of the circle and r be the radius of the circle.
1. Draw OP, OA, OB, and AB.
2. Since PA is a secant, we can apply the secant-tangent theorem:
- PA * PB = OA * OB
- 9 * (9 + 7) = 13 * (13 + r)
- 144 = 169 + 13r
- 13r = 169 - 144
- 13r = 25
- r = 25/13
- r ≈ 1.92 cm
Therefore, the radius of the circle is approximately 1.92 cm.
ANSWER: The correct option is (B) 5 cm (approximated to two decimal places).
- Point P is outside the circle.
- Distance between point P and the center of the circle is 13 cm.
- A secant drawn from point P intersects the circle at points A and B.
- PA = 9 cm and AB = 7 cm.
To find: The radius of the circle.
Solution:
Let O be the center of the circle and r be the radius of the circle.
1. Draw OP, OA, OB, and AB.
2. Since PA is a secant, we can apply the secant-tangent theorem:
- PA * PB = OA * OB
- 9 * (9 + 7) = 13 * (13 + r)
- 144 = 169 + 13r
- 13r = 169 - 144
- 13r = 25
- r = 25/13
- r ≈ 1.92 cm
Therefore, the radius of the circle is approximately 1.92 cm.
ANSWER: The correct option is (B) 5 cm (approximated to two decimal places).
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P is a point outside a circle and is 13 cm away from its centre. A secant drawn from the point P intersect the circle at points A and B in such a way that PA = 9 cm and AB = 7 cm. The radius of the circle is: (SSC CGL 2nd Sit. 2012)a)5.5 cmb)5 cmc)4 cmd)4.5 cmCorrect answer is option 'B'. Can you explain this answer?
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