Mathematics
The radii of two concentric circles are 17 cm and 10 cm; a line PQRS cuts the larger circle at P and S and the smaller circle at Q and R. If QR = 12 cm, calculate PQ.
Circles
17 Likes
Answer
Draw OM ⊥ QR.
In right △OQM,
⇒ OQ2 = OM2 + QM2
⇒ 102 = OM2 + 62
⇒ OM2 = 100 - 36
⇒ OM2 = 64
⇒ OM = = 8 cm.
In right △POM,
⇒ PO2 = OM2 + PM2
⇒ 172 = 82 + PM2
⇒ PM2 = 289 - 64
⇒ PM2 = 225
⇒ PM = = 15 cm.
From figure,
PQ = PM - QM = 15 - 6 = 9 cm.
Hence, PQ = 9 cm.
Answered By
13 Likes
Related Questions
In the adjoining figure, a chord PQ of a circle with center O and radius 15 cm is bisected at M by a diameter AB. If OM = 9 cm, find the lengths of :
(i) PQ
(ii) AP
(iii) BP.
A chord of length 48 cm is at a distance of 10 cm from the centre of a circle. If another chord of length 20 cm is drawn in the same circle, find its distance from the center of the circle.
In the figure (i) given below, two circles with centers C, D intersect in points P, Q. If length of common chord is 6 cm and CP = 5 cm, DP = 4 cm, calculate the distance CD correct to two decimal places.
In the figure (ii) given below, P is a point of intersection of two circles with centers C and D. If the st. line APB is parallel to CD, prove that AB = 2CD.
