If a point P is 17 cm from the center of a circle of radius 8 cm, then the length of the tangent drawn to the circle from the point P is
- 10 cm
- 12 cm
- 15 cm
- 14 cm
The Correct Option is C
Solution and Explanation
We are given a circle with radius 8 cm and a point \( P \) that is 17 cm away from the center of the circle. We need to find the length of the tangent drawn from point \( P \) to the circle. We can use the Pythagorean theorem to solve this. In the right triangle formed by the radius of the circle, the line joining the center \( O \) to the point \( P \), and the tangent from point \( P \) to the circle, we know:
The distance from \( P \) to \( O \) is 17 cm.
The radius of the circle (distance from \( O \) to \( A \)) is 8 cm.
The length of the tangent (from \( P \) to \( A \)) is what we need to find. Let the length of the tangent be \( x \). According to the Pythagorean theorem: \[ x^2 + 8^2 = 17^2. \] \[ x^2 + 64 = 289. \] \[ x^2 = 289 - 64 = 225. \] \[ x = \sqrt{225} = 15 \text{ cm}. \]
The correct option is (C): \(15\ cm\)
Top Questions on Circles
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In the following figure chord MN and chord RS intersect at point D. If RD = 15, DS = 4, MD = 8, find DN by completing the following activity:
Activity :
\(\therefore\) MD \(\times\) DN = \(\boxed{\phantom{SD}}\) \(\times\) DS \(\dots\) (Theorem of internal division of chords)
\(\therefore\) \(\boxed{\phantom{8}}\) \(\times\) DN = 15 \(\times\) 4
\(\therefore\) DN = \(\frac{\boxed{\phantom{60}}}{8}\)
\(\therefore\) DN = \(\boxed{\phantom{7.5}}\)
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