Two Parallel Tangents of a Circle Meet a Third Tangent

Here we will prove that two parallel tangents of a circle meet a third tangent at points A and B. Prove that AB subtends a right angle at the centre.

Two Parallel Tangents of a Circle Meet a Third Tangent


Given: CA, AB and EB are tangents to a circle with centre O. CA ∥ EB.

To prove: ∠AOB = 90°.




1. AO bisects ∠CAD

⟹ ∠OAD = \(\frac{1}{2}\)∠CAD

1. The line joining the centre of a circle to the point of intersection of two tangents bisects the angle between the tangents.

2. BO bisects ∠DBE

⟹ ∠OBD = \(\frac{1}{2}\)∠DBE.

2. As in statement 1.

3. ∠CAD + ∠DBE = 180°

⟹ \(\frac{1}{2}\)∠CAD + \(\frac{1}{2}\)∠DBE = \(\frac{1}{2}\)180°

⟹ ∠OAD + ∠OBD = 90°.

3. Co. interior angles and CA ∥ EB.

Using statements 1 and 2 in statement 3.

4. Therefore, ∠AOB = 180° - (∠OAD + ∠OBD)

                            = 180° - 90°

                            = 90°. (proved).

4. Sum of three angles of a triangle is 180°.

10th Grade Math

From Two Parallel Tangents of a Circle Meet a Third Tangent 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.

Share this page: What’s this?

Recent Articles

  1. Relation between Diameter Radius and Circumference |Problems |Examples

    Apr 22, 24 05:19 PM

    Relation between Radius and Diameter of a Circle
    Relation between diameter radius and circumference are discussed here. Relation between Diameter and Radius: What is the relation between diameter and radius? Solution: Diameter of a circle is twice

    Read More

  2. Circle Math | Terms Related to the Circle | Symbol of Circle O | Math

    Apr 22, 24 01:35 PM

    Circle using a Compass
    In circle math the terms related to the circle are discussed here. A circle is such a closed curve whose every point is equidistant from a fixed point called its centre. The symbol of circle is O. We…

    Read More

  3. Preschool Math Activities | Colorful Preschool Worksheets | Lesson

    Apr 21, 24 10:57 AM

    Preschool Math Activities
    Preschool math activities are designed to help the preschoolers to recognize the numbers and the beginning of counting. We believe that young children learn through play and from engaging

    Read More

  4. Months of the Year | List of 12 Months of the Year |Jan, Feb, Mar, Apr

    Apr 20, 24 05:39 PM

    Months of the Year
    There are 12 months in a year. The months are January, February, march, April, May, June, July, August, September, October, November and December. The year begins with the January month. December is t…

    Read More

  5. What are Parallel Lines in Geometry? | Two Parallel Lines | Examples

    Apr 20, 24 05:29 PM

    Examples of Parallel Lines
    In parallel lines when two lines do not intersect each other at any point even if they are extended to infinity. What are parallel lines in geometry? Two lines which do not intersect each other

    Read More