A chord of length 16 cm is drawn in a circle of diameter 20 cm. Calculate its distance from the centre of the circle.

Given: Length of the chord AC = 16 cm. Diameter of the circle = 20 cm. Radius of the circle r = = 10 cm. To prove: Distance of the chord from the center of the circle = OB. Construction: Draw OB ⊥ AC, where O is the center of the circle. Join OA. Proof: B is the midpoint of AC, as OB is perpendicular to the chord AC. AB = AC = x 16 cm = 8 cm In Δ OAB, ∠B = 90° Using Pythagoras theorem, ∴ OA2 = OB2 + AB2 ⇒ (10)2 = OB2 + (8)2 ⇒ 100 = OB2 + 64 ⇒ OB2 = 100 - 64 ⇒ OB2 = 36 ⇒ OB = ⇒ OB = 6 cm Hence, the distance of the chord from the center of the circle is 6 cm.

In triangle ABC, D is mid-point of AB and P is any point on BC. If CQ parallel to PD meets AB at Q, prove that:
2 x area (△ BPQ) = area (△ ABC)

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In △ ABC, D is a point on side AB and E is a point on AC. If DE is parallel to BC, and BE and CD intersect each other at point O; prove that :
(i) area (△ ACD) = area (△ ABE)
(ii) area (△ OBD) = area (△ OCE)

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In the given figure, the diameter CD of a circle with centre O is perpendicular to the chord AB.
If AB = 8 cm and CM = 2 cm, find the radius of the circle.

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Two chords AB and CD of lengths 24 cm and 10 cm respectively of a circle are parallel. If the chords lie on the same side of the centre and distance between them is 7 cm, find the length of a diameter of the circle.

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Mathematics

A chord of length 16 cm is drawn in a circle of diameter 20 cm. Calculate its distance from the centre of the circle.

Circles

Related Questions

In triangle ABC, D is mid-point of AB and P is any point on BC. If CQ parallel to PD meets AB at Q, prove that:
2 x area (△ BPQ) = area (△ ABC)

In △ ABC, D is a point on side AB and E is a point on AC. If DE is parallel to BC, and BE and CD intersect each other at point O; prove that :
(i) area (△ ACD) = area (△ ABE)
(ii) area (△ OBD) = area (△ OCE)

In the given figure, the diameter CD of a circle with centre O is perpendicular to the chord AB.
If AB = 8 cm and CM = 2 cm, find the radius of the circle.

Two chords AB and CD of lengths 24 cm and 10 cm respectively of a circle are parallel. If the chords lie on the same side of the centre and distance between them is 7 cm, find the length of a diameter of the circle.

Mathematics

A chord of length 16 cm is drawn in a circle of diameter 20 cm. Calculate its distance from the centre of the circle.

Circles

Related Questions

In triangle ABC, D is mid-point of AB and P is any point on BC. If CQ parallel to PD meets AB at Q, prove that:2 x area (△ BPQ) = area (△ ABC)

In △ ABC, D is a point on side AB and E is a point on AC. If DE is parallel to BC, and BE and CD intersect each other at point O; prove that :(i) area (△ ACD) = area (△ ABE)(ii) area (△ OBD) = area (△ OCE)

In the given figure, the diameter CD of a circle with centre O is perpendicular to the chord AB.If AB = 8 cm and CM = 2 cm, find the radius of the circle.

Two chords AB and CD of lengths 24 cm and 10 cm respectively of a circle are parallel. If the chords lie on the same side of the centre and distance between them is 7 cm, find the length of a diameter of the circle.

In triangle ABC, D is mid-point of AB and P is any point on BC. If CQ parallel to PD meets AB at Q, prove that:
2 x area (△ BPQ) = area (△ ABC)

In △ ABC, D is a point on side AB and E is a point on AC. If DE is parallel to BC, and BE and CD intersect each other at point O; prove that :
(i) area (△ ACD) = area (△ ABE)
(ii) area (△ OBD) = area (△ OCE)

In the given figure, the diameter CD of a circle with centre O is perpendicular to the chord AB.
If AB = 8 cm and CM = 2 cm, find the radius of the circle.