# 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.

Solution:

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

To prove: ∠AOB = 90°.

Proof:

 Statement Reason 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°.

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.

## Recent Articles

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

Apr 22, 24 05:19 PM

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

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

Apr 22, 24 01:35 PM

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…

3. ### Preschool Math Activities | Colorful Preschool Worksheets | Lesson

Apr 21, 24 10:57 AM

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

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

Apr 20, 24 05:39 PM

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…