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If two tangents are drawn from a point outside a circle, and the lengths of the

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Question: If two tangents are drawn from a point outside a circle, and the lengths of the tangents are 7 cm and 7 cm, what is the distance from the point to the center of the circle?

Options:

  1. 7√2
  2. 7
  3. 14
  4. 10

Correct Answer: 7√2

Solution: 

The distance from the point to the center is equal to the length of the tangent divided by cos(45°), which is 7√2.

If two tangents are drawn from a point outside a circle, and the lengths of the

Practice Questions

Q1
If two tangents are drawn from a point outside a circle, and the lengths of the tangents are 7 cm and 7 cm, what is the distance from the point to the center of the circle?
  1. 7√2
  2. 7
  3. 14
  4. 10

Questions & Step-by-Step Solutions

If two tangents are drawn from a point outside a circle, and the lengths of the tangents are 7 cm and 7 cm, what is the distance from the point to the center of the circle?
  • Tangents to a Circle – Understanding the properties of tangents drawn from an external point to a circle, including the fact that they are equal in length.
  • Distance from Point to Center – Applying the Pythagorean theorem to find the distance from the external point to the center of the circle using the tangent length.
  • Trigonometric Ratios – Using trigonometric ratios, specifically cosine, to relate the tangent length and the distance to the center.
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