Contact of Two Circles

Here we will prove that two circles with centres X and Y touch externally at T. A straight line is drawn through T to cut the circles at M and N. Proved that XM is parallel to YN.

Contact of Two Circles

Solution:

Given: Two circles with centres X and Y touch externally at T. A straight line is drawn through T to cut the circles at M and N.

To prove: XM ∥ YN.

Construction: Join T to X and Y.

Proof:

Statement

Reason

1. In ∆XMT, ∠XMT = ∠XTM

1. XM = XT, being radii.

2. In ∆YNT, ∠YNT = ∠YTN

2. YN = YT, being radii.

3. XTY is a straight line.

3. The point of contact of two circles lies on the straight line joining their centres.

4. ∠XTM = ∠YTN

4. Vertically opposite angles.

5. ∠XMT = ∠YNT

5. From statements 1, 2 and 4.

6. XM ∥ YN. (Proved)

6. Alternate angles are equal, using statement 5.





10th Grade Math

From Contact of Two Circles to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

RSS

  1. 2nd Grade Geometry Worksheet | Plane and Solid Shapes | Point | Line

    Dec 12, 24 09:20 AM

    Curved Line and Straight Line
    2nd grade geometry worksheet

    Read More

  2. Types of Lines |Straight Lines|Curved Lines|Horizontal Lines| Vertical

    Dec 09, 24 10:39 PM

    Types of Lines
    What are the different types of lines? There are two different kinds of lines. (i) Straight line and (ii) Curved line. There are three different types of straight lines. (i) Horizontal lines, (ii) Ver…

    Read More

  3. Points and Line Segment | Two Points in a Curved Surface | Curve Line

    Dec 09, 24 01:08 AM

    Curved Lines and Straight Line
    We will discuss here about points and line segment. We know when two lines meet we get a point. When two points on a plane surface are joined, a straight line segment is obtained.

    Read More

  4. Solid Shapes | Basic Geometric Shapes | Common Solid Figures | Plane

    Dec 08, 24 11:19 PM

    Solid Shapes
    We will discuss about basic solid shapes. We see a variety of solid objects in our surroundings. Solid objects have one or more shapes like the following. Match the objects with similar shape.

    Read More

  5. 2nd grade math Worksheets | Free Math Worksheets | By Grade and Topic

    Dec 07, 24 03:38 PM

    2nd Grade Math Worksheet
    2nd grade math worksheets is carefully planned and thoughtfully presented on mathematics for the students.

    Read More