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MathematicsCircleTangent & NormalMedium2 minQB

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Passage / Comprehension

A circle of diameter 2 is tangent to both coordinate axes, with P=(0,4). Each successive diameter-2 circle is tangent to the x-axis, the preceding tangent from P and a new tangent from P crossing the positive x-axis further right. Let x_n be the x-intercept of the nth tangent.

A circle of diameter 2 is tangent to both axes; $P = (0, 4)$ . Each successive diameter-2 circle is tangent to the $x$ -axis, the preceding tangent from $P$ , and a new tangent from $P$ that crosses the positive $x$ -axis further right. Let $x_{n}$ be the $x$ -intercept of the $n$ th tangent. Find $x_{2}, x_{3}, x_{4}$ as fractions.

Options:

Answer:

Solution:

Start $x_{1} = 3$ from the 3-4-5 right triangle, then apply the recurrence: $x_{2} = 15/2, x_{3} = 63/4, x_{4} = 255/8$ .

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Tangent & Normal

⏱ 2mℹ️ Source: QB

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