O is the centre of the circle and length of the chord is 8 cm seg OP _| chord AB. if l(OP)= 3cm then find the radius of the circle?
Answers
Step-by-step explanation:
Given o is the center of circle ,OM=3 cm and AB=8 cm
Join O to A and B
In figure OM show that the perpendicular from center O on cord AB
WE know that Perpendicular from the Center of a Circle to a Chord Bisects the Chord.
Then AM=BM
So AM=BM=2AB=28=4cm
ΔAOM
(AO)2=(AM)2+(OM)2=(4)2+(3)2=16+9=25
⇒AO=5cm
Then AO is the radius of circle
Given : O is the center of the circle, and length of the chord AB is 8 cm
OP ⊥ AB
length of OP = 3 cm
To Find : Radius of the circle
Solution:
AB is the chord
O is center of circle
OP ⊥ AB
Hence P is mid point of AB
=> AP = BP = AB/2 = 8/2 = 4 cm
OP = 3cm
Applying Pythagorean theorem
OA² = OP² + AP²
=> OA² = 3² + 4²
=> OA² = 25
=> OA = 5 cm
Radius of circle = 5 cm
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