Advertisements
Advertisements
प्रश्न
Two circle with centres A and B, and radii 5 cm and 3 cm, touch each other internally. If the perpendicular bisector of the segment AB meets the bigger circle in P and Q; find the length of PQ.
उत्तर
If two circles touch internally, then distance between their centres is equal to the difference of their radii.
So, AB = (5 − 3) cm = 2 cm.
Also, the common chord PQ is the perpendicular bisector of AB.
Therefore, AC = CB = `1/2` AB = 1 cm
In right ΔACP, we have AP2 = AC2 + CP2
`=>` 52 = 12 + CP2
`=>` CP2 = 25 – 1 = 24
`=> CP = sqrt(24)= 2 sqrt(6) cm`
Now, PQ = 2 CP
= `2 xx 2sqrt(6) cm`
= `4sqrt(6) cm`
APPEARS IN
संबंधित प्रश्न
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 given figure, M is the centre of the circle. Chords AB and CD are perpendicular to each other. If ∠MAD = x and ∠BAC = y :
- express ∠AMD in terms of x.
- express ∠ABD in terms of y.
- prove that : x = y.
In following figure , AB , a chord of the circle is of length 18 cm. It is perpendicularly bisected at M by PQ.
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.
A chord of length 6 cm is drawn in a circle of radius 5 cm.
Calculate its distance from the center of the circle.
M and N are the mid-points of two equal chords AB and CD respectively of a circle with center O.
Prove that: (i) ∠BMN = ∠DNM
(ii) ∠AMN = ∠CNM
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.
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.
