Chapter 6.3, Problem 38E

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

The center of a circle of radius 3 in. is at a distance of 20 in. from the center of a circle of radius 9 in. what is the exact length of common internal tangent

*(HINT: Use similar triangles to find OD and DP. Then apply the Pythagorean Theorem twice.)*

*Exercises 38, 39*

To determine

**To find:**

The find value of

Explanation

Given that, the center of a circle of radius 3 in. is at a distance of 20 in. from the center of a circle of radius 9 in.

That is

The diagrammatic representation is given below,

Since

Using the vertical angle theorem to get the following,

Therfore,

If two triangles are similar, then the ration of any two corresponding segments (such as altitudes, medians, or angle bisectors) equals the ratio of any two corresponding sides.

We know that,

Substitute this in the above equation to get the following,

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Sect-6.1 P-11ESect-6.1 P-12ESect-6.1 P-13ESect-6.1 P-14ESect-6.1 P-15ESect-6.1 P-16ESect-6.1 P-17ESect-6.1 P-18ESect-6.1 P-19ESect-6.1 P-20ESect-6.1 P-21ESect-6.1 P-22ESect-6.1 P-23ESect-6.1 P-24ESect-6.1 P-25ESect-6.1 P-26ESect-6.1 P-27ESect-6.1 P-28ESect-6.1 P-29ESect-6.1 P-30ESect-6.1 P-31ESect-6.1 P-32ESect-6.1 P-33ESect-6.1 P-34ESect-6.1 P-35ESect-6.1 P-36ESect-6.1 P-37ESect-6.1 P-38ESect-6.1 P-39ESect-6.1 P-40ESect-6.1 P-43ESect-6.2 P-1ESect-6.2 P-2ESect-6.2 P-3ESect-6.2 P-4ESect-6.2 P-5ESect-6.2 P-6ESect-6.2 P-7ESect-6.2 P-8ESect-6.2 P-9ESect-6.2 P-10ESect-6.2 P-11ESect-6.2 P-12ESect-6.2 P-13ESect-6.2 P-14ESect-6.2 P-15ESect-6.2 P-16ESect-6.2 P-17ESect-6.2 P-18ESect-6.2 P-19ESect-6.2 P-20ESect-6.2 P-21ESect-6.2 P-22ESect-6.2 P-23ESect-6.2 P-24ESect-6.2 P-25ESect-6.2 P-26ESect-6.2 P-27ESect-6.2 P-28ESect-6.2 P-29ESect-6.2 P-30ESect-6.2 P-31ESect-6.2 P-32ESect-6.2 P-33ESect-6.2 P-34ESect-6.2 P-35ESect-6.2 P-36ESect-6.2 P-37ESect-6.2 P-38ESect-6.2 P-39ESect-6.2 P-40ESect-6.2 P-41ESect-6.2 P-42ESect-6.2 P-43ESect-6.2 P-44ESect-6.2 P-45ESect-6.2 P-46ESect-6.2 P-47ESect-6.2 P-48ESect-6.2 P-49ESect-6.3 P-1ESect-6.3 P-2ESect-6.3 P-3ESect-6.3 P-4ESect-6.3 P-5ESect-6.3 P-6ESect-6.3 P-7ESect-6.3 P-8ESect-6.3 P-9ESect-6.3 P-10ESect-6.3 P-11ESect-6.3 P-12ESect-6.3 P-13ESect-6.3 P-14ESect-6.3 P-15ESect-6.3 P-16ESect-6.3 P-17ESect-6.3 P-18ESect-6.3 P-19ESect-6.3 P-20ESect-6.3 P-21ESect-6.3 P-22ESect-6.3 P-23ESect-6.3 P-24ESect-6.3 P-25ESect-6.3 P-26ESect-6.3 P-27ESect-6.3 P-28ESect-6.3 P-29ESect-6.3 P-30ESect-6.3 P-31ESect-6.3 P-32ESect-6.3 P-33ESect-6.3 P-34ESect-6.3 P-35ESect-6.3 P-36ESect-6.3 P-37ESect-6.3 P-38ESect-6.3 P-39ESect-6.3 P-40ESect-6.3 P-41ESect-6.3 P-42ESect-6.3 P-43ESect-6.3 P-44ESect-6.3 P-45ESect-6.3 P-46ESect-6.3 P-47ESect-6.3 P-48ESect-6.3 P-49ESect-6.3 P-50ESect-6.4 P-1ESect-6.4 P-2ESect-6.4 P-3ESect-6.4 P-4ESect-6.4 P-5ESect-6.4 P-6ESect-6.4 P-7ESect-6.4 P-8ESect-6.4 P-9ESect-6.4 P-10ESect-6.4 P-11ESect-6.4 P-12ESect-6.4 P-13ESect-6.4 P-14ESect-6.4 P-15ESect-6.4 P-16ESect-6.4 P-17ESect-6.4 P-18ESect-6.4 P-19ESect-6.4 P-20ESect-6.4 P-21ESect-6.4 P-22ESect-6.4 P-23ESect-6.4 P-24ESect-6.4 P-25ESect-6.4 P-26ESect-6.4 P-27ESect-6.4 P-28ESect-6.4 P-29ESect-6.4 P-30ESect-6.4 P-31ESect-6.4 P-32ESect-6.4 P-33ESect-6.4 P-34ESect-6.4 P-35ESect-6.4 P-36ESect-6.4 P-37ESect-6.4 P-38ESect-6.4 P-39ESect-6.4 P-40ESect-6.4 P-41ESect-6.CR P-1CRSect-6.CR P-2CRSect-6.CR P-3CRSect-6.CR P-4CRSect-6.CR P-5CRSect-6.CR P-6CRSect-6.CR P-7CRSect-6.CR P-8CRSect-6.CR P-9CRSect-6.CR P-10CRSect-6.CR P-11CRSect-6.CR P-12CRSect-6.CR P-13CRSect-6.CR P-14CRSect-6.CR P-15CRSect-6.CR P-16CRSect-6.CR P-17CRSect-6.CR P-18CRSect-6.CR P-19CRSect-6.CR P-20CRSect-6.CR P-21CRSect-6.CR P-22CRSect-6.CR P-23CRSect-6.CR P-24CRSect-6.CR P-25CRSect-6.CR P-26CRSect-6.CR P-27CRSect-6.CR P-28CRSect-6.CR P-29CRSect-6.CR P-30CRSect-6.CR P-31CRSect-6.CR P-32CRSect-6.CR P-33CRSect-6.CR P-34CRSect-6.CR P-35CRSect-6.CT P-1CTSect-6.CT P-2CTSect-6.CT P-3CTSect-6.CT P-4CTSect-6.CT P-5CTSect-6.CT P-6CTSect-6.CT P-7CTSect-6.CT P-8CTSect-6.CT P-9CTSect-6.CT P-10CTSect-6.CT P-11CTSect-6.CT P-12CTSect-6.CT P-13CTSect-6.CT P-14CTSect-6.CT P-15CTSect-6.CT P-16CT

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