Advertisements
Advertisements
प्रश्न
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
उत्तर
Drop OM and O'N perpendicular on AB and OM' and O'N' perpendicular on CD.
∴ OM, O'N, OM' and O'N' bisect AP, PB, CQ and QD respectively.
( Perpendicular is drawn from the center of a circle to a chord bisects it. )
∴ MP = `1/2"AP" , "PN" = 1/2"BP" , "M'Q" = 1/2"CQ" , "QN"' = 1/2"QD"`
Now, OO' = MN = MP + PN = `1/2( "AP + BP" ) = 1/2"AB"` ...(i)
and OO' = M'N' = M'Q + QN' = `1/2( "CQ + QD" ) = 1/2"CD"` ...(ii)
By (i) and (ii),
AB = CD.
APPEARS IN
संबंधित प्रश्न
AB and CD are two parallel chords of a circle such that AB = 24 cm and CD = 10 cm. If the
radius of the circle is 13 cm. find the distance between the two chords.
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
In Δ ABC, the perpendicular from vertices A and B on their opposite sides meet (when produced) the circumcircle of the triangle at points D and E respectively. Prove that: arc CD = arc CE
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, AD is a straight line, OP ⊥ AD and O is the centre of both circles. If OA = 34cm, OB = 20 cm and OP = 16 cm;
find the length of AB.
In the following figure, the line ABCD is perpendicular to PQ; where P and Q are the centers of the circles.
Show that:
(i) AB = CD ;
(ii) AC = BD.
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.
AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24 cm. If the chords are on the opposite sides of the centre and the distance between them is 17 cm, find the radius of the circle.
