Advertisements
Advertisements
प्रश्न
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.
उत्तर
Let AB be the chord and O be the center of the circle.
Let OC be the perpendicular drawn from O to AB.
We know, that the perpendicular to a chord, from the center of a circle, bisects the chord.
∴ AB = 8 cm
⇒ AC = CB = `"AB"/2`
⇒ AC = CB = `8/2`
⇒ AC = CB = 4 cm
In OCA,
OA2 = OC2 + AC2 ...( By Pythagoras theorem )
⇒ OA2 = ( 4 )2 + ( 3 )2 = 25
⇒ OA = 5 cm
Hence, radius oof the circle is 5 cm.
APPEARS IN
संबंधित प्रश्न
A chord of length 8 cm is drawn at a distance of 3 cm from the centre of a circle. Calculate the radius of the circle.
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
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
A chord of length 8cm is drawn inside a circle of radius 6cm. Find the perpendicular distance of the chord from the centre of the circle.
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.
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, 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.
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.
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.
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.
