Multiple choice

A point $P$ is $25cm$ from the centre of a circle. The radius of the circle is $7cm$ and length of the tangent drawn from $P$ to the circle is $x$ cm. The value of $x=$ is

  1. $20cm$
  2. $24cm$
  3. $18cm$
  4. $12cm$
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B Correct answer
Explanation

The tangent, radius, and line to the center form a right triangle where the distance to the center (25) is the hypotenuse. x^2 + 7^2 = 25^2. x^2 = 625 - 49 = 576. x = 24.

AI explanation

The radius, the tangent, and the segment connecting the external point to the center form a right triangle. By the Pythagorean theorem, the length of the tangent x is calculated as the square root of (25^2 - 7^2). This evaluates to the square root of (625 - 49), which is the square root of 576. The value of x is 24 cm.

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