Advertisements
Advertisements
प्रश्न
The radius of a circle is 13 cm and the length of one of its chord is 10 cm. Find the distance of the chord from the centre.
उत्तर
Let AB be a chord of a circle with centre O and radius 13cm such that AB = 10 cm.
From O, draw OL ⊥ AB. Join OA.
Since, the perpendicular from the centre of a circle to a chord bisects the chord.
∴ AL = LB = `1/2`AB = 5 cm.
Now, in right triangle OLA, we have
OA2 = OL2 + AL2
⇒ 132 = OL2 + 52
⇒ 132 - 52 = OL2
⇒ OL2 = 144
⇒ OL = 12 cm
Hence, the distance of the chord from the centre is 12 cm.
APPEARS IN
संबंधित प्रश्न
A chord of length 24 cm is at a distance of 5 cm from the centre of the circle. Find the length of the chord of the same circle which is at a distance of 12 cm from the centre.
Two circle with centres A and B, and radii 5 cm and 3 cm, touch each other internally. If the perpendicular bisector of the segment AB meets the bigger circle in P and Q; find the length of PQ.
In following figure , AB , a chord of the circle is of length 18 cm. It is perpendicularly bisected at M by PQ.
In the given figure, M is the centre of the circle. Chords AB and CD are perpendicular to each other.
If ∠MAD = x and ∠BAC = y : express ∠ABD in terms of y.
A chord of length 6 cm is drawn in a circle of radius 5 cm.
Calculate its distance from the center of the circle.
Two parallel chords are drawn in a circle of diameter 30.0 cm. The length of one chord is 24.0 cm and the distance between the two chords is 21.0 cm;
find the length of another chord.
In the following figure; P and Q are the points of intersection of two circles with centers O and O'. If straight lines APB and CQD are parallel to OO';
prove that: (i) OO' = `1/2`AB ; (ii) AB = CD
In the given figure, l is a line intersecting the two concentric circles, whose common center is O, at the points A, B, C, and D. Show that AB = CD.
AB is a diameter of a circle with centre C = (- 2, 5). If A = (3, – 7). Find
(i) the length of radius AC
(ii) the coordinates of B.
In Fig. O is the centre of the circle with radius 5 cm. OP⊥ AB, OQ ⊥ CD, AB || CD, AB = 8 cm and CD = 6 cm. Determine PQ.
