1 / 7

Tangent Circles: Theorems and Practice Examples

Understand and verify tangents to circles using Pythagorean Theorem, Theorem 10.1, and practice exercises. Find radii, lengths, and solve for values. Detailed solutions provided for guided learning.

marykoenig
Download Presentation

Tangent Circles: Theorems and Practice Examples

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. In the diagram, PTis a radius of P. Is STtangent to P ? SOLUTION Use the Converse of the Pythagorean Theorem. Because 122 + 352 = 372,PSTis a right triangle and STPT. So, STis perpendicular to a radius of Pat its endpoint on P. By Theorem 10.1, STis tangent to P. EXAMPLE 4 Verify a tangent to a circle

  2. In the diagram, Bis a point of tangency. Find the radiusr of C. SOLUTION You know from Theorem 10.1 that AB BC, so ABCis a right triangle. You can use the Pythagorean Theorem. EXAMPLE 5 Find the radius of a circle AC2 = BC2 + AB2 Pythagorean Theorem (r + 50)2 = r2 + 802 Substitute. r2 + 100r + 2500 = r2 + 6400 Multiply. 100r = 3900 Subtract from each side. r = 39 ft. Divide each side by 100.

  3. RSis tangent to Cat Sand RTis tangent to Cat T. Find the value of x. Tangent segments from the same point are EXAMPLE 6 Find the radius of a circle SOLUTION RS= RT 28 = 3x + 4 Substitute. 8 = x Solve for x.

  4. 7.IsDEtangent to C? ANSWER Yes – The length of CE is 5 because the radius is 3 and the outside portion is 2. That makes ∆CDE a 3-4-5 Right Triangle. So DE and CD are for Examples 4, 5 and 6 GUIDED PRACTICE

  5. 8. ST is tangent toQ.Find the value of r. SOLUTION You know from Theorem 10.1 that STQS, so QSTis a right triangle. You can use the Pythagorean Theorem. for Examples 4, 5 and 6 GUIDED PRACTICE

  6. for Examples 4, 5 and 6 GUIDED PRACTICE QT2 = QS2 + ST2 Pythagorean Theorem (r + 18)2 = r2 + 242 Substitute. r2 + 36r + 324 = r2 + 576 Multiply. 36r = 252 Subtract from each side. r = 7 Divide each side by 36.

  7. 9. Find the value(s)of x. Tangent segments from the same point are for Examples 4, 5 and 6 GUIDED PRACTICE SOLUTION 9= x2 Substitute. +3= x Solve for x.

More Related