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A point P is 25 cm from the centre of a circle. The radius of the circle is 7 cm and length of the tangent drawn from P to the circle is x cm. The value of x =
  • a)
    20 cm
  • b)
    24 cm
  • c)
    18 cm
  • d)
    12 cm.
Correct answer is option 'B'. Can you explain this answer?
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A point P is 25 cm from the centre of a circle. The radius of the circ...
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A point P is 25 cm from the centre of a circle. The radius of the circ...
Given information
- A point P is 25 cm from the centre of a circle.
- The radius of the circle is 7 cm.
- Length of the tangent drawn from P to the circle is x cm.

To find
The value of x.

Solution
Let O be the centre of the circle and PT be the tangent drawn from P to the circle as shown below.

[INSERT IMAGE]

We can observe that OP is the hypotenuse of the right-angled triangle OPT. Therefore, using Pythagoras theorem, we can find the length of PT as follows.

OP² = OT² + PT²
(25)² = (7)² + PT²
625 = 49 + PT²
PT² = 625 - 49
PT² = 576
PT = √576
PT = 24 cm

Therefore, the value of x is 24 cm.

Answer: Option B.
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A point P is 25 cm from the centre of a circle. The radius of the circle is 7 cm and length of the tangent drawn from P to the circle is x cm. The value of x =a)20 cmb)24 cmc)18 cmd)12 cm.Correct answer is option 'B'. Can you explain this answer?
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