Advertisements
Advertisements
Question
In a circle, AB and CD are two parallel chords with centre O and radius 10 cm such that AB = 16 cm and CD = 12 cm determine the distance between the two chords?
Advertisements
Solution
Length of the chord (AB) = 16 cm
∴ AF = `1/2 xx 16`
= 8 cm
Length of the chord (CD) = 12 cm
∴ CE = `1/2 xx 12`
= 6 cm
In the right ΔOCE,
OE2 = OC2 – CE2
= 102 – 62
= 100 – 36
= 64
OE = `sqrt(64)`
= 8 cm
In the right ΔOAF,
OF2 = OA2 – AF2
= 102 – 82
= 100 – 64
= 36
OE = `sqrt(36)`
= 6 cm
Distance between the two chords
= OE + OF
= 8 + 6
= 14 cm
APPEARS IN
RELATED QUESTIONS
Fill in the blank
Circles having the same centre and different radii are called ...........................circles.
In the given figure, if ∠ABC = 45°, then ∠AOC =
In the given figure, chords AD and BC intersect each other at right angles at a point P. If ∠DAB = 35°, then
The point of concurrence of all angle bisectors of a triangle is called the ______.
In the above figure, `square`XLMT is a rectangle. LM = 21 cm, XL = 10.5 cm. Diameter of the smaller semicircle is half the diameter of the larger semicircle. Find the area of non-shaded region.
In an equilateral triangle, prove that the centroid and center of the circum-circle (circumcentre) coincide.
Circles with centres A, B and C touch each other externally. If AB = 36, BC = 32, CA = 30, then find the radii of each circle.
From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is ______
From the figure, identify three radii.
Is every chord of a circle also a diameter?
