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Chapter 9: Q6. (page 335)

RS炉 and TU炉are common internal tangents to the circles. If RZ=4路7 and ZU=7路3, Find RS and TU.

Short Answer

Expert verified

Value of,RS=12

And, TU=12.

Step by step solution

01

Step 1. Given information.

The figure:

RZ=4.7 And ZU=7.3

02

Step 2. Concept Used.

Theorem 9路1 Corollary:

Tangents to a circle from a point are congruent.

03

Step 3. Consider the given figure for further solution.

From the above figure it is clear that RZ炉 and TZ炉are tangents to the smaller circle from the common point Z,so by theorem 9路1 corollary, it can be said that:

TZ=RZ=4.7 鈥�.. (1)

Similarly, UZ炉andSZ炉are tangents to the bigger circle from the common point Z,so by theorem 9路1 corollary, it can be said that:

SZ=UZ=7.3 鈥�.. (2)

04

Step 4. Thus, from (1) and (2).

RS=RZ+ZS=4.7+7.3=12

And

TU=TZ+ZU=4.7+7.3=12

Therefore, Value of,RS=12, and TU=12.

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