If the length of the tangent drawn from a point P out side the circle is 15 cm and radius of circle is 8 cm, then distance of point P from the centre of circle is :

Options

A. 7cm
B. 23 cm
C. 17 cm
D. 7.5 cm

Answer

To find the distance of point P from the center of the circle (denoted as O), we can use the Pythagorean theorem. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Length of the tangent (PA) = 15 cm
- Radius of the circle (OA) = 8 cm

### Step 2: Set up the right triangle
In the right triangle formed by the radius (OA), the tangent (PA), and the distance from point P to the center of the circle (PO), we can denote:
- OA = radius = 8 cm (one leg of the triangle)
- PA = tangent = 15 cm (the other leg of the triangle)
- PO = distance from point P to the center O (the hypotenuse)

### Step 3: Apply the Pythagorean theorem
According to the Pythagorean theorem:
\[ PO^2 = PA^2 + OA^2 \]

### Step 4: Substitute the values
Substituting the known values into the equation:
\[ PO^2 = 15^2 + 8^2 \]
\[ PO^2 = 225 + 64 \]

### Step 5: Calculate the sum
Now, calculate the sum:
\[ PO^2 = 289 \]

### Step 6: Find PO by taking the square root
To find PO, take the square root of both sides:
\[ PO = \sqrt{289} \]
\[ PO = 17 \text{ cm} \]

### Final Answer
The distance of point P from the center of the circle is **17 cm**.

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