a chord of length 48 cm is drawn in a circle of radius 25 cm . calculate its distance from the center of the circle
Answers
AB is the chord of the circle with centre O and radius OA
OM is perpendicular to AB
Therefore,
AB = 48 cm
OA = 25 cm
OM ⊥ AB
M is the mid-point of AB
AM = 1/2 AB = ½ × 48 = 24 cm
Now right ∆OAM,
OA2 = OM2 + AM2
(by Pythagoras Axiom)
(25)2 = OM² + (24)²
OM2 = (25)² – (24)² = 625 – 576
= 49 = (7)²
OM = 7 cm
Step-by-step explanation:
A chord of length 48 cm is drawn in a circle of radius 25 cm . Calculate its distance from the center of the circle.
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⟼AB is the chord of the circle with centre O and radius OA
✰ OM is perpendicular to AB
⟼Therefore,
✰ AB = 48 cm
✰ OA = 25 cm
✰ OM ⊥ AB
⟼M is the mid-point of AB
✰ AM = 1/2 AB = ½ × 48 = 24 cm
⟼Now right ∆OAM,
✰ OA2 = OM2 + AM2
(by Pythagoras Axiom)
✰ (25)2 = OM² + (24)²
✰ OM2 = (25)² – (24)² = 625 – 576
= 49 = (7)²
⟼OM = 7 cm
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