Advertisements
Advertisements
Question
Two chords AB, CD of lengths 16 cm and 30 cm, are parallel. If the distance between AB and CD is 23 cm. Find the radius of the circle.
Solution
Let AB and CD be the two parallel chords of a circle with centre O and radius r cm.
OM ⊥ AB and ON ⊥ CD
AM = `1/2"AB" = 1/2 xx 16` = 8 cm
CN = `1/2"CD" = 1/2 xx 30` = 15 cm
Let OM = x cm, MN = 23 cm
so ON = (23 - x) cm
OA = OC = r cm
In Δ OAM,
OA2 = AM2 + OM2
⇒ r2 = (8)2 + (x)2 ....(i)
In Δ OCN,
OC2 = CN2 + ON2
⇒ r2 = (15)2 + (23 - x )2 ....(ii)
From (i) and (ii),
x2 + 64 = 225 + (23 - x)2
⇒ x2 + 64 = 225 + 529 - 46x + x2
⇒ 46x = 225 + 529 - 64
⇒ 46x = 690
⇒ x = 15 cm
From (i),
r2 = (8)2 + (15)2
r2 = 64 + 225
r2 = 289
⇒ r = 17 cm
Hence, the radius of a circle is 17 cm.
APPEARS IN
RELATED QUESTIONS
AB and CD are two equal chords of a circle with centre O which intersect each other at right
angle at point P. If OM⊥ AB and ON ⊥ CD; show that OMPN is a square.
Given O is the centre of the circle and ∠AOB = 70°. Calculate the value of:
- ∠OCA,
- ∠OAC.
In the following figure, O is the centre of the circle. Find the values of a, b and c.
In the following figure, O is the centre of the circle. Find the values of a, b, c and d
Calculate:
- ∠CDB,
- ∠ABC,
- ∠ACB.
The sides AB and DC of a cyclic quadrilateral ABCD are produced to meet at E; the sides DA and CB are produced to meet at F. If ∠BEC = 42° and ∠BAD = 98°; Calculate :
(i) ∠AFB (ii) ∠ADC
In following fig., chords PQ and RS of a circle intersect at T. If RS = 18cm, ST = 6cm and PT = 18cm, find the length of TQ.
If two chords of a circle are equally inclined to the diameter through their point of intersection, prove that the chords are equal.
In the adjoining figure, PQ is the diameter, chord SR is parallel to PQ. Give ∠ PQR = 58°.
Calculate:
(i) ∠ RPQ,
(ii) ∠ STP ( T is a point on the minor arc)
In the diagram given alongside, AC is the diameter of the circle, with centre O. CD and BE are parallel. ∠ AOB = 80° and ∠ ACE = 10°. Calculate: (i) ∠ BEC (ii) ∠ BCD (iii) ∠ CED.
