A secant is drawn from a point P to a circle so that it meets the circle first at A, then goes through the centre, and leaves the circle at B. If the length of the tangent from P to the circle is 12 cm, and the radius of the circle is 5 cm, then the distance from P to A is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 8 cm.
| Understanding/Application |
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The radius of the circle = 5 cm Let the distance from P to A be x. PB is the secant and PV is the tangent to the circle from exterior point P. PV2 = PA. PB 122 = PA. (PA + AB) 144 = x(x + 10) 144 = x2 + 10x x2 + 10x - 144 = 0 x2 + 18x - 8x - 144 = 0 x(x + 18) - 8(x + 18) = 0 (x - 8) (x + 18) = 0 x = 8, -18 |
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x cannot be negative. Distance from P to A = 8 cm |