When you have a circle, a tangent is perpendicular to its radius. It touches (intersects) the circle at only one point and looks like a line that sits just outside the circle’s circumference. The fact that it is perpendicular will come in useful in our calculations as we can then make use the Pythagorean theorem.
How to find the tangent of a circle
In the questions you’ll have to answer in this lesson, you’ll either be given the tangent or you’ll have to look for it. Some tangent properties that you should keep in mind to help you solve problems include:
1) A tangent is perpendicular to the radius at the point of tangency.
2) Tangent segments to an external point of a circle are equal.
3) The angle between a tangent and a chord is equal to the inscribed angle on the opposite side of that chord.
You’ll see these properties in use in the practice problems coming up when dealing with a (or several) tangent line on a circle.
A tangent to a circle must form a perpendicular line from the point of tangency to the center of the circle. In this lesson, we will learn how to use this property, along with others such as, chord properties, to solve questions.
In the diagram below, BC is a diameter, and AB is tangent to the circle at point B. OB = 6 cm, and AB = 8 cm.
Find the length of the diameter.
Justify if △CBD is a right angle.
Find the length of the chord DC.
Find the length of AC.
If there is a straight line connecting point D and point O, what type of triangle is △BOD?
The furthest the hammer can travel in a hammer throw game is when the hammer travels along a tangent. If a hammer lands 62 m away from the athlete, how far did the hammer travel along a tangent? (Hint: The hammer is 1.2 m in length.)