Question:medium

Let \(C_1\) and \(C_2\) be concentric circles such that the diameter of \(C_1\) is 2 cm longer than that of \(C_2\). If a chord of \(C_1\) has length 6 cm and is a tangent to \(C_2\), then the diameter, in cm, of \(C_1\) is
[This Question was asked as TITA]

Updated On: Jan 15, 2026
  • 10 cm
  • 12 cm
  • 15 cm
  • 18 cm
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The Correct Option is A

Solution and Explanation

Given: \( d + 2 = D \Rightarrow r + 1 = R \)

In the provided diagram, the small circle's radius is denoted by \( r \). Consequently:

  • \( OT = r \) represents the radius of the smaller circle.
  • \( OB = r + 1 = R \) represents the radius of the larger circle.
  • The line segment AB is tangent to the smaller circle at point T, meaning it is perpendicular to the radius OT.
  • Thus, \( OT \perp AB \).
  • Furthermore, OT bisects AB, resulting in \( TB = \frac{6}{2} = 3 \, \text{cm} \).

Applying the Pythagorean theorem to the right-angled triangle \( \triangle OTB \):

\[ OT^2 + TB^2 = OB^2 \]

Substituting the known values:

\[ r^2 + 3^2 = (r + 1)^2 \]

Expanding the equation:

\[ r^2 + 9 = r^2 + 2r + 1 \]

Simplifying by canceling \( r^2 \) from both sides:

\[ 9 = 2r + 1 \Rightarrow 2r = 8 \Rightarrow r = 4 \]

With \( r = 4 \), the radius of the larger circle is \( R = r + 1 = 5 \).

The diameter of the larger circle is calculated as: \[ D = 2R = 2 \times 5 = \mathbf{10 \, \text{cm}} \]

Correct option: (A) 10 cm

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In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
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