In the figure, the line segment ST is tangent to two circles at S and...

JAMB 1993

In the figure, the line segment ST is tangent to two circles at S and T. O and Q are the centres of the circles wih OS = 5cm. QT = 2cm and OR = 14cm. Find ST

A. 7 \(\sqrt{3}\)cm
B. 12.9cm
C. \(\sqrt{87}\)cm
D. 7cm

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Correct Answer: Option B

Explanation

SQ² + OS² = OQ² + 5² = 14²

SQ² = 14² - 5²

196 - 25 = 171

ST² + TQ² = SQ²

ST² + 2² = 171

ST² = 171 - 4

= 167

ST = \(\sqrt{167}\)

= 12.92 = 12.9cm

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