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Chapter 9: Q22. (page 337)

Prove theorem 9.2

Short Answer

Expert verified

A tangent can touch a circle at only one point.

Step by step solution

01

Step 1. Statement.

A tangent can touch a circle at only one point.

02

Step 2. Draw the figure.

Consider a line in the plane of a circle perpendicular to a radius at its outer endpoint.

In the below figure line lis the plane of circle with center Qand l鈯�QR.

03

Step 3. Concept used.

Suppose lis not tangent to circle then lis touching the circle at some other point P, then QP=QR.

This is because both are radius, and they both make same angle.

Since, l鈯�QR then l鈯�QP also but 螖QPRcannot have two 90掳angle.

Therefore, lcannot touch the circle at two points, so line ltouch the circle at only R.

Therefore, by definition of tangent line lis tangent to circle.

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Most popular questions from this chapter

For each exercise draw a circle and inscribe the polygon in the circle.

c. An obtuse triangle.

TR炉and TS炉are tangents to 鈯�Ofrom T;

m鈭�RTS=36

a.Copy the diagram. Draw RS炉and find m鈭�TSRand m鈭�TRS.

b.Draw radii OS炉and OR炉and find m鈭�ORSand m鈭�OSR.

c.Find m鈭�ROS.

d.Does your result in part csupport one of your conclusions about angles in Classroom Exercise 5?Explain.

Circles Pand Qhave radii 6 and 2 and are tangent to each other. Find length of their common external tangent AB.炉

Three circles are shown. How many circles tangent to all three of the given circles can be drawn ?

a. Which pair of circles shown above are externally tangent?

b. Which pair are internally tangent?
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