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 :
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Step-by-Step Solution
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: 252=625 and 72=49.
Step 4: Isolate PT2
To find the value of PT2, subtract 49 from 625.
Step 5: Calculate PT2
Performing the subtraction, we get PT2=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.