Please tell with explanation
Answers
Answer:
Step-by-step explanation:
NOTE: Pls refer to the attachment given under the explanation
In the figure, O is the centre of the circle.
Seg AB is the diameter.
Seg CD is the chord.
We have given that,
AB = 10 cm
CD = 8 cm
Now,
Radius of circle ( AO ) = ½ × Diameter of circle ( AB )
⇒ AO = ½ × 10
⇒ AO = 5 cm
∴ Radius of circle = 5 cm
∴ OC = 5 cm - - ( 1 )
Now,
OE ⊥ CD - - [ Construction ]
We know that,
A perpendicular drawn from centre of circle to a chord, bisects the chord.
∴ CE = DE = ½ × CD
⇒ CE = ½ × 8
⇒ CE = 4 cm - - ( 2 )
Now, in △OEC, ∠OEC = 90°
∴ ( OC )² = ( CE )² + ( OE )² - - [ Pythagors theorem ]
⇒ ( 5 )² = ( 4 )² + ( OE )² - - [ From ( 1 ) & ( 2 ) ]
⇒ 25 = 16 + ( OE )²
⇒ ( OE )² = 25 - 16
⇒ ( OE )² = 9
⇒ OE = √9 - - [ Taking square roots ]
∴ OE = 3 cm
∴ The distance of the chord from the centre of the circle is 3 cm.
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Additional Information:
1. Property of chord and centre of the circle:
A perpendicular drawn from the centre of the circle to any chord of the circle bisects the chord.
2. The minimum distance between any two points is perpendicular distance.
3. All radii of the same circle are equal in measures.
4. Diameter is twice the radius of the circle.
Hope it helps!!
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