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

সঠিক উত্তর

TQ = TR

গণিত বিষয়ের কিছু ইম্পোরটেন্ট প্রশ্ন

মেধা যাচাই করুন

এই প্রশ্নটি সহ গণিত বিষয়ের আরও কিছু গুরুত্বপূর্ণ প্রশ্ন আছে

গণিত1 নম্বর

১ + ৫ + ৯ + ........... +৮১ = ?

প্র্যাকটিস সেশন

গণিত

গণিত বিষয়ের আরও প্রশ্ন দিয়ে নিজেকে যাচাই করুন

শুরু করুন

বিস্তারিত ব্যাখ্যা

<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.

<h2>Geometric Properties of Tangents</h2>

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.

<h2>Mathematical Reasoning</h2>

Let's denote the lengths of TQ and TR as follows:

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:

Therefore, the correct answer to the multiple-choice question is:

TQ = TR

<h2>References and Further Reading</h2>

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

</body> </html>

সকল অপশন

রেফারেন্স মাত্র

TQ = TR সঠিক উত্তর

T = TR

TQ = 2 Tk.

TQ > TR