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

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

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