The given figure shows a circle with centre O and 6 cm radius. It is
also given that BC = 16 cm. What is the length of AB?
Answers
length of AB = 12 cm , a circle with centre O and 6 cm radius. BC = 16 cm
Step-by-step explanation:
Join OP
OP ⊥ AC (as AC is tangent)
OP = OB = 6 cm Radius
OC = BC - OB
=> OC = 16 - 6 = 10 cm
comparing Δ CPO & ΔCBA
∠CPO = ∠CBA = 90°
∠C = ∠C ( common)
=> Δ CPO ≈ ΔCBA
=> CP/CB = OP/AB = OC/AC
=> CP / 16 = 6/AB = 10/AC
=> AB = 96/CP
AP = AB ( equal Tangent)
AC = AP + CP = 96/CP + CP
AC² = AB² + BC²
=> (96/CP + CP)² = (96/CP)² + 16²
=> (96/CP)² + CP² + 192 = (96/CP)² + 256
=> CP² = 64
=> CP = 8
or (CP² = OC² - OP² = 10² - 6² = 8² => CP = 8)
CP / 16 = 6/AB
=> 8/16 = 6/AB
=> AB = 96/8
=> AB = 12
length of AB = 12 cm
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