In the figure, points P, B and Q are points of
contact of the respective tangents, line QA Co
parallel to the line PC. If QA = 7.2cm, P C = 5cm,
find the radius of the circle
Answers
Radius of circle = 6 cm
Step-by-step explanation:
∠OQA = ∠OPC = ∠OBA = ∠OBC = 90° ( Tangent)
=> ∠QOB + ∠QAB = 180°
∠POB + ∠PCB = 180°
QA ║ PC
=> ∠QAB + ∠PCB = 180°
=> ∠QAB = ∠POB & ∠QOB = ∠PCB
QA = BA = 7.2 cm ( equal tangent)
PC = BC = 5 cm ( equal Tangent)
OQ = OB = OP = Radius
=> ΔQAB ≈ ΔPOB
=> QA/OP = AB/PB = QB/PB
=> 7.2/R = 7.2/R = QB/PB
ΔQOB ≈ ΔPCB
=> OQ/CP = OB/BC = QB/PB
=> R/5 = R/5 = QB/PB
=> 7.2/R = R/5
=> R² = 36
=> R = 6 cm
Radius = 6 cm
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