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.
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. |
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.