Diameter of a circle is 10cm and length of a chord is 8cm. Find the distance of the chord from the centre.
Answers
Answer:
The distance of the chord from the centre of the circle is 3 cm.
Step-by-step-explanation:
NOTE: Refer to the attachment for the diagram.
In 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.
─────────────────────
Additional Information:
1. Property of chord and centre of circle:
A perpendicular drawn from centre of 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 circle.
Answer:
The answer is 13 cm.
Hope it helps.
