Multiple choice

Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on outer circle construct the pair of tangents to the other. Measure the length of a tangent and verify it by actual calculation.

  1. 3 cm

  2. 4 cm

  3. 5 cm

  4. 6 cm
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B Correct answer
Explanation

The radius of the inner circle is 3 cm and the outer is 5 cm. A tangent from the outer circle to the inner circle forms a right triangle with the radius of the inner circle (3 cm) and the radius of the outer circle (5 cm) as the hypotenuse. Tangent length = sqrt(5^2 - 3^2) = sqrt(25 - 9) = sqrt(16) = 4 cm.

AI explanation

The length of a tangent drawn from an external point on the outer circle to the inner circle can be found using the Pythagorean theorem, as the radius of the inner circle is perpendicular to the tangent at the point of contact. We use the right triangle with the outer circle's radius of 5 cm as the hypotenuse and the inner circle's radius of 3 cm as one leg. The length of the tangent is the square root of (25 minus 9), which equals the square root of 16, giving a length of 4 cm.

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