The length of the tangent drawn from a point P, whose distance from the centre of a circle is 25 cm, and the radius of the circle is 7 cm, is :

Step 1: Identify the geometric relationship

When a tangent is drawn from an external point P to a circle at point T, the radius OT is perpendicular to the tangent PT. This forms a right-angled triangle OPT, where OP is the hypotenuse, OT is the radius, and PT is the length of the tangent. We can apply the Pythagorean theorem to this triangle.

Step 2: Substitute the given values

We are given that the distance from the center O to point P is 25 cm, so $OP = 25$ cm. The radius of the circle is 7 cm, so $OT = 7$ cm. Substitute these values into the Pythagorean theorem.

Step 3: Calculate the squares

Calculate the squares of the given lengths: $25^2 = 625$ and $7^2 = 49$.

Step 4: Isolate $PT^2$

To find the value of $PT^2$, subtract 49 from 625.

Step 5: Calculate $PT^2$

Performing the subtraction, we get $PT^2 = 576$.

Step 6: Find the length of PT

To find the length of the tangent PT, take the square root of 576.

Step 7: Final Answer

The square root of 576 is 24. Therefore, the length of the tangent is 24 cm.

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