Advertisements
Advertisements
प्रश्न
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.
उत्तर
Join OA and OC.
Since the perpendicular from the centre of the circle to a chord bisects the chord. Therefore, P and Q are midpoints of AB and CD respectively.
Consequently, AP = PB = `1/2"AB"` = 3 cm.
and CQ = QD = `1/2`CD = 4 cm
In right triangles OAP and OCQ, we have
OA2 = OP2 + AP2 and OC2 = OQ2 + CQ2
⇒ 52 = OP2 + 32 and 52 = OQ2 + 42
⇒ OP2 = 52 - 32 and OQ2 = 52 - 42
⇒ OP2 = 16 and OQ2 = 9
⇒ OP = 4 and OQ = 3
∴ PQ = OP + OQ = (4 + 3) cm = 7 cm.
APPEARS IN
संबंधित प्रश्न
A chord of length 6 cm is drawn in a circle of radius 5 cm. Calculate its distance from the centre of the circle.
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.
Two chords AB and AC of a circle are equal. Prove that the centre of the circle lies on the bisector of angle BAC.
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 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.
A chord of length 24 cm is at a distance of 5 cm from the center of the circle. Find the length of the chord of the same circle which is at a distance of 12 cm from the center.
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.
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 C = (- 2, 5). If A = (3, – 7). Find
(i) the length of radius AC
(ii) the coordinates of B.
