Subscribe to our ▶️ YouTube channel 🔴 for the latest videos, updates, and tips.
Two Tangents are Drawn to a Circle from an External Point
We will prove that the tangents MX and MY are drawn to a circle with centre O from an external point M. Prove that ∠XMY = 2∠OXY.
Solution:
Proof:
|
Statement |
Reason |
|
1. In ∆MXY, MX = MY. |
1. Tangents drawn to a circle from an external point are equal. |
|
2. ∠MXY = ∠MYX = x°. |
2. From statement 1. |
|
3. ∠XMY = 180° - x°. |
3.Sum of three angles of a triangle is 180°. |
|
4. OX ⊥ XM, i.e., ∠OXM = 90°. |
4. Radius ⊥ tangent. |
|
5. ∠OXY = 90° - ∠MXY ⟹ ∠OXY = 90° - x° ⟹ 2∠OXY = 180° - 2x° |
5. From the figure. |
|
6. Therefore, ∠XMY = 2∠OXY. (Proved). |
6. From statements 3 and 5. |
From Two Tangents are Drawn to a Circle from an External Point 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.