A point P is 13 xm from the centre of a circle . Radius of the circle is 5 cm . A tangent is drawn from point P to the circle , then the length of the tangent is :

Options

A. 10
B. 11
C. 12
D. 13

Answer

To find the length of the tangent drawn from point P to the circle, we can use the following steps:

### Step 1: Identify the given values
- Distance from point P to the center of the circle (OP) = 13 cm
- Radius of the circle (r) = 5 cm

### Step 2: Use the tangent-segment theorem
According to the tangent-segment theorem, the length of the tangent (PT) from point P to the circle can be calculated using the formula:
\[ PT = \sqrt{OP^2 - r^2} \]
where:
- \( OP \) is the distance from point P to the center of the circle,
- \( r \) is the radius of the circle.

### Step 3: Substitute the values into the formula
Substituting the known values into the formula:
\[ PT = \sqrt{(13)^2 - (5)^2} \]

### Step 4: Calculate the squares
Calculating the squares:
\[ PT = \sqrt{169 - 25} \]

### Step 5: Perform the subtraction
Now, perform the subtraction:
\[ PT = \sqrt{144} \]

### Step 6: Calculate the square root
Finally, calculate the square root:
\[ PT = 12 \, \text{cm} \]

Thus, the length of the tangent from point P to the circle is **12 cm**.

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