Advertisements
Advertisements
प्रश्न
The radius of a circle is 13 cm and the length of one of its chords is 24 cm.
Find the distance of the chord from the center.
उत्तर
To find: OM
Given that AB = 24 cm
Since OM ⊥ AB
⇒ OM bisects AB
So, AM = 12 cm
In right ⇒ OMA,
OA2 = OM2 + AM2
OM2 = OA2 - AM2
OM2 = 132 - 122
OM2 = 25
OM2 = 5 cm
Hence, the distance of the chord from the centre is 5 cm.
APPEARS IN
संबंधित प्रश्न
In the following figure, the line ABCD is perpendicular to PQ; where P and Q are the centres of
the circles. Show that:
(i) AB = CD,
(ii) AC = BD.
From a point P outside a circle, with centre O. tangents PA and PB are drawn as following fig., Prove that ∠ AOP = ∠ BOP and OP is the perpendicular bisector of AB.
In the given figure, O is the center of the circle. AB and CD are two chords of the circle. OM is perpendicular to AB and ON is perpendicular to CD. AB = 24 cm, OM = 5 cm, ON = 12 cm, 
Find the :
(i) the radius of the circle
(ii) length of chord CD.
A chord CD of a circle whose center is O is bisected at P by a diameter AB. Given OA = OB = 15 cm and OP = 9 cm.
Calculate the lengths of: (i) CD ; (ii) AD ; (iii) CB.
In a circle of radius 17 cm, two parallel chords of lengths 30 cm and 16 cm are drawn. Find the distance between the chords,
if both the chords are:
(i) on the opposite sides of the centre;
(ii) on the same side of the centre.
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, OD is perpendicular to the chord AB of a circle whose center is O. If BC is a diameter, show that CA = 2 OD.
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 O and radius OD is perpendicular to AB. If C is any point on arc DB, find ∠ BAD and ∠ ACD.
In the figure given below, O is the centre of the circle. AB and CD are two chords of the circle. OM is perpendicular to AB and ON is perpendicular to CD.
AB = 24 cm, OM = 5 cm, ON = 12 cm. Find the
(i) radius of the circle
(ii) length of chord CD.
