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In the figure the line segment ST is tangent to... - JAMB Mathematics 1993 Question

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
correct option: b
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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