Two circles of equal radii touch externally at a point P . Form a point T on the target at P target TQ and TR are drawn to the circles with points of contact Q and R respectively. The relations of TQ and TR is
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সঠিক উত্তর
TQ = TR
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বিষয়ভিত্তিক সাপ্তাহিক মডেল টেস্ট - গণিত
মডেল টেস্ট দিন, সম্পূর্ণ বিনামূল্যে
লগইন করে মডেল টেস্ট শুরু করুনব্যাখ্যা
<html lang="en"> <head> <meta charset="UTF-8"> <meta name="viewport" content="width=device-width, initial-scale=1.0"> <title>Explanation of Two Circles Touching Externally</title> <style> body { font-family: Arial, sans-serif; line-height: 1.6; margin: 20px; } .equation { font-family: "Times New Roman", Times, serif; } </style> </head> <body> <h1>Explanation of the Relationship Between TQ and TR</h1>
Let's analyze the given problem step-by-step to understand why TQ = TR is the correct answer.
<h2>Problem Summary</h2>We have two circles of equal radii that touch externally at a point P. From a point T on the common tangent at P, tangent segments TQ and TR are drawn to the circles with points of contact Q and R respectively.
<h2>Diagram and Geometry</h2>To correctly visualize the problem, consider the following setup:
- Two circles with centers O<sub>1</sub> and O<sub>2</sub> and radius r.
- The circles touch externally at point P.
- A common external tangent at P intersects a point T.
- Tangent segments TQ and TR are drawn from point T touching the circles at points Q and R respectively.
We use the following key properties of tangents to circles:
- Tangent segments drawn from an external point to a circle are equal in length.
- Tangent segments from a common external point to two touching circles are equal, due to the congruence of the tangents.
Let's denote the lengths of TQ and TR as follows:
<div class="equation"> TQ = TR </div>This is due to the fact that both TQ and TR are tangent segments drawn from the same external point T to the points of contact Q and R on respective circles. Because tangents from an external point to a circle are equal, and the circles touch externally, segments TQ and TR must be equal.
<h2>Conclusion</h2>Thus, we conclude that the correct relationship between TQ and TR is:
<div class="equation"> TQ = TR </div>Therefore, the correct answer to the multiple-choice question is:
- TQ = TR
For more in-depth understanding of circle tangents and properties, you can refer to renowned geometry textbooks such as:
- “Geometry for Dummies” by Mark Ryan
- “Khan Academy” for online tutorials about circle properties
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