Tangent - Perpendicular to Radius
Here we will prove that the tangent at any point of a circle and the radius through the point are perpendicular to each other.
Given:
A circle with centre O in which OP is a radius. XPY is a tangent drawn to the circle at the point P.
To prove: OP ⊥ XY.
Construction: On XY take any point Q, other than P. Join O to Q.
Proof:
|
Statement |
Reason |
|
1. OQ > OP ⟹ OP is the shortest line segment that can be drawn to the tangent XY from O. |
1. Every point on the tangent, other than P, lies outside the circle. |
|
2. OP ⊥ XY. (Proved) |
2. The shortest line segment, drawn to a line from a point outside it, is perpendicular to the line. |
Note:
1. One and only one tangent can be drawn to a circle at a given point on the circumference because only one perpendicular can be drawn to Op through the point P.
2. The perpendicular to a tangent through its point of contact passes through centre of the circle because only one perpendicular, OP, can be drawn to the line XY through the point P.
3. The radius drawn perpendicular to the tangent passes through the point of contact because only one perpendicular, Op can be drawn to XY from the point O.
From Tangent - Perpendicular to Radius 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
-
Place Value | Place, Place Value and Face Value | Grouping the Digits
Oct 04, 24 09:47 AM
The place value of a digit in a number is the value it holds to be at the place in the number. We know about the place value and face value of a digit and we will learn about it in details. We know th… -
Worksheet on Subtraction | Practice the Questions | Free Answers
Oct 04, 24 01:28 AM
In worksheet on subtraction, all grade students can practice the questions on subtracting numbers with more than two digits. This exercise sheet on subtraction can be practiced by the students -
Subtraction Word Problems - 2-Digit Numbers | Subtraction Problems
Oct 03, 24 03:22 PM
Understand the concept on subtraction word problems - 2-digit numbers for the second grade. Read the question carefully to subtract the two-digit numbers to find the differences and follow the -
Worksheet on Checking Subtraction Using Addition | Free Answers | Math
Oct 03, 24 02:22 PM
Here we can use addition to check the answer for the subtraction. Subtract ans check your answer. Find the difference and check your answer using addition. -
Check for Subtraction and Addition | Checking Subtraction | Problems
Oct 03, 24 01:13 PM
We will learn to check for subtraction and addition answers after solving. Difference of two numbers is correct when the sum of the subtrahend number and the difference is equal to the minuend.
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.