The length of tangent drawn to a circle with radius 7 cm from a point 25 cm away the centre , is

Options

A. 24 cm
B. 27 cm
C. 26 cm
D. 25 cm

Answer

To find the length of the tangent drawn to a circle with a radius of 7 cm from a point that is 25 cm away from the center of the circle, we can use the Pythagorean theorem. Here’s how to solve the problem step by step:

### Step 1: Understand the Geometry
We have a circle with center O and radius r = 7 cm. There is a point P outside the circle, which is 25 cm away from the center O. We need to find the length of the tangent PT from point P to the point of tangency T on the circle.

### Step 2: Identify the Right Triangle
The line segment OP (from the center O to point P) is the hypotenuse of the right triangle OPT, where OT is the radius (7 cm) and PT is the tangent we want to find. According to the properties of tangents, the angle ∠OTP is 90 degrees.

### Step 3: Apply the Pythagorean Theorem
According to the Pythagorean theorem:
\[ OP^2 = OT^2 + PT^2 \]
Where:
- OP = 25 cm (the distance from the center to the point)
- OT = 7 cm (the radius of the circle)
- PT = length of the tangent (which we need to find)

### Step 4: Substitute the Known Values
Substituting the known values into the equation:
\[ 25^2 = 7^2 + PT^2 \]
Calculating the squares:
\[ 625 = 49 + PT^2 \]

### Step 5: Rearrange the Equation
Now, rearranging the equation to solve for PT^2:
\[ PT^2 = 625 - 49 \]
\[ PT^2 = 576 \]

### Step 6: Take the Square Root
To find PT, we take the square root of both sides:
\[ PT = \sqrt{576} \]
Calculating the square root:
\[ PT = 24 \text{ cm} \]

### Conclusion
The length of the tangent drawn from point P to the circle is **24 cm**.

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