Advertisements
Advertisements
प्रश्न
The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at distance 4 cm from the centre, what is the distance of the other chord from the centre?
Advertisements
उत्तर
Let AB and CD be two parallel chords in a circle centered at O. Join OB and OD.
Distance of smaller chord AB from the centre of the circle = 4 cm
OM = 4 cm
MB = AB/2 = 6/2 = 3cm
In ΔOMB,
OM2 + MB2 = OB2
(4)2 + (3)2 = OB2
16 + 9 = OB2
OB2 = 25
`OB = sqrt25`
OB = 5cm
In ΔOND,
OD = OB = 5cm (Radii of the same circle)
ND = CD/2 = 8/2 = 4cm
ON2 + ND2 = OD2
ON2 + (4)2 = (5)2
ON2 = 25 - 16 = 9
ON = 3
Therefore, the distance of the bigger chord from the centre is 3 cm.
APPEARS IN
संबंधित प्रश्न
If the non-parallel sides of a trapezium are equal, prove that it is cyclic.
Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see the given figure). Prove that ∠ACP = ∠QCD.
Prove that a cyclic parallelogram is a rectangle.
Prove that the line of centres of two intersecting circles subtends equal angles at the two points of intersection.
Let the vertex of an angle ABC be located outside a circle and let the sides of the angle intersect equal chords AD and CE with the circle. Prove that ∠ABC is equal to half the difference of the angles subtended by the chords AC and DE at the centre.
ABCD is a parallelogram. The circle through A, B and C intersect CD (produced if necessary) at E. Prove that AE = AD.
AC and BD are chords of a circle which bisect each other. Prove that (i) AC and BD are diameters; (ii) ABCD is a rectangle.
If the two sides of a pair of opposite sides of a cyclic quadrilateral are equal, prove that its diagonals are equal.
In the given figure, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If ∠DBC = 55° and ∠BAC = 45°, find ∠BCD.
If a pair of opposite sides of a cyclic quadrilateral are equal, prove that its diagonals are also equal.
