EXAMPLE 4 Verify a tangent to a circle

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Presentation transcript:

EXAMPLE 4 Verify a tangent to a circle In the diagram, PT is a radius of P. Is ST tangent to P ? SOLUTION Use the Converse of the Pythagorean Theorem. Because 122 + 352 = 372, PST is a right triangle and ST PT . So, ST is perpendicular to a radius of P at its endpoint on P. By Theorem 10.1, ST is tangent to P.

Find the radius of a circle EXAMPLE 5 Find the radius of a circle In the diagram, B is a point of tangency. Find the radius r of C. SOLUTION You know from Theorem 10.1 that AB BC , so ABC is a right triangle. You can use the Pythagorean Theorem. 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.

Find the radius of a circle EXAMPLE 6 Find the radius of a circle RS is tangent to C at S and RT is tangent to C at T. Find the value of x. SOLUTION RS = RT Tangent segments from the same point are 28 = 3x + 4 Substitute. 8 = x Solve for x.

GUIDED PRACTICE for Examples 4, 5 and 6 7. Is DE tangent 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

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

GUIDED PRACTICE for Examples 4, 5 and 6 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.

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