Advertisements
Advertisements
प्रश्न
In a circle of radius 10 cm, AB and CD are two parallel chords of lengths 16 cm and 12 cm respectively.
Calculate the distance between the chords, if they are on:
(i) the same side of the center.
(ii) the opposite sides of the center.
उत्तर
Given that AB = 16 cm and CD = 12 cm
So, AL = 8 cm and CM = 6 cm ....( ⊥ from the center to the chord bisects the chord )
In right triangle OLA and OMC,
By Pythagoras theorem,
OA2 = OL2 + AL2 and OC2 = OM2 + Cm2
102 = OL2 + 82 and 102 = OM2 + 62
OL2 = 100 - 64 and OM2 = 64
OL2 = 6 cm and OM2 = 8 cm
(i) In the first case, distance between AB and CD is
LM= OM - OL = 8 - 6 = 2 cm
(ii) In the second case , distance between AB and CD is
LM = OM + OL = 8 + 6 = 14 cm
APPEARS IN
संबंधित प्रश्न
The radius of a circle is 17.0 cm and the length of perpendicular drawn from its centre to a chord is 8.0 cm. Calculate the length of the chord.
A chord CD of a circle whose centre is O, is bisected at P by a diameter AB.
Given OA = OB = 15 cm and OP = 9 cm. calculate the length of:
(i) CD (ii) AD (iii) CB
The figure shows two concentric circles and AD is a chord of larger circle.
Prove that: AB = CD
Two chords of lengths 10cm and 24cm are drawn parallel o each other in a circle. If they are on the same side of the centre and the distance between them is 17cm, find the radius of the circle.
From a point P outside a circle, with centre O, tangents PA and PB are drawn. Prove that:
OP is the ⊥ bisector of chord AB.
A chord of length 8 cm is drawn at a distance of 3 cm from the center of the circle.
Calculate the radius of the circle.
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.
Two chords AB and CD of a circle are parallel and a line L is the perpendicular bisector of AB. Show that L bisects 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 of radius 5 cm. OP ⊥ AB, OQ ⊥ CD, AB || CD, AB = 6 cm and CD = 8 cm. Determine PQ.
