Advertisements
Advertisements
Question
In a circle with centre O, AB and CD are two diameters perpendicular to each other. The length of chord AC is
Options
2AB
- \[\sqrt{2}\]
- \[\frac{1}{2}AB\]
- \[\frac{1}{\sqrt{2}}AB\]
Solution
We are given a circle with centre at O and two perpendicular diameters AB and CD.
We need to find the length of AC.
We have the following corresponding figure:
Since, AB = CD (Diameter of the same circle)
Also, ∠AOC = 90°
And, AO = `(AB)/2`
Here, AO = OC (radius)
In ΔAOC
`AC^2 = AO^2 + OC^2 = AO^2 + AO^2`
`= ((AB)/2)^2 + ((AB)/2)^2`
`AC^2 = (AB^2)/2`
`AC = (AB)/(sqrt(2))`
APPEARS IN
RELATED QUESTIONS
If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords.
If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C, and D, prove that AB = CD (see given figure).
Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is 6m each, what is the distance between Reshma and Mandip?
A circular park of radius 20m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. Find the length of the string of each phone.
true or false
A circle has only finite number of equal chords.
Two chords AB and CD of lengths 5 cm and 11 cm respectively of a circle are parallel to each other and are opposite side of its center. If the distance between AB and CD is 6 cm. Find the radius of the circle.
In a circle of radius 17 cm, two parallel chords are drawn on opposite side of a diameter. The distance between the chords is 23 cm. If the length of one chord is 16 cm, then the length of the other is
Two congruent circles with centres O and O′ intersect at two points A and B. Then ∠AOB = ∠AO′B.
If two equal chords of a circle intersect, prove that the parts of one chord are separately equal to the parts of the other chord.
Two equal chords AB and CD of a circle when produced intersect at a point P. Prove that PB = PD.
