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EXAMPLE 4

In the diagram, PT is a radius of P . Is ST tangent to P ?. SOLUTION.

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EXAMPLE 4

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  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.

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