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Chapter 9: Q4. (page 335)

Given PA炉and PB炉 are tangents to 鈯�o.

Use the diagram at the right to explain how the corollary on page 333

follows from Theorem9-1.

Short Answer

Expert verified

a. Tangent PA is congruent to tangent PB.

Step by step solution

01

Step 1. Given information:

The figure is given.

02

Step 2. Concept used:

We used the theorem 9-1.

03

Step 3. Applying the concept:

If the line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangents.

Then,

OA鈯�PAOB鈯�PB

Then once can say that,

鈭�PAO=90鈭�鈭�PBO=90鈭�
It is required to prove two triangles are congruent.

Consider in 鈻�PAO and 鈻�PBO,

OA=OB鈭�PAO=鈭�PBOPO=OP

(Radius of a circle is equal)

(Both the angles are )

(Common side of a triangle)

So, it implies that

鈻�PAO鈮�鈻�PBO ( Side-Angle-Side Rule)

Since the corresponding parts of congruent triangles are congruent.

Therefore, the following holds good PA and PB.

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