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 answer is 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