Question : 
Triangle ABC is circumscribed around circle D. Segments AQ, BR, and SC measure 13,10.5, and 6 cm, respectively. The perimeter of triangle ABC is:
Option 1: 29.5 cm
Option 2: 59 cm
Option 3: 108 cm
Option 4: 15 cm
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Correct Answer: 59 cm
Solution :
Given: Triangle ABC is circumscribed around circle D
Segments AQ = 13 cm
BR = 10.5 cm
SC = 6 cm
$\because$ The tangents drawn from an external point to the circle are equal in length,
AQ = AS = 13 cm
BR = QB = 10.5 cm
SC = CR = 6 cm
The perimeter of triangle ABC = AQ + QB + BR + RC + SC + AS = 13 + 10.5 + 10.5 + 6 + 6 + 13 = 59 cm
$\therefore$ The perimeter of the triangle ABC is 59 cm.
Hence, the correct answer is 59 cm.
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