Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
From a point T outside a circle of centre O, tangents TP and TQ are drawn to the circle. Prove that OT is the right bisector of line segment PQ.
Write True or False. Give reason for your answer.
A circle has only finite number of equal chords.
A point P is 26 cm away from O of circle and the length PT of the tangent drawn from P to the circle is 10 cm. Find the radius of the circle.
true or false
A chord of a circle, which is twice as long is its radius is a diameter of the circle.
A chord of length 14 cm is at a distance of 6 cm from the centre of a circle. The length of another chord at a distance of 2 cm from the centre of the circle is
In the given figure, PA and PB are tangents to the circle from an external point P. CD is another tangent touching the circle at Q. If PA = 12 cm, QC = QD = 3 cm, then find PC + PD.
In the given circle with diameter AB, find the value of x.
A, B, C are any points on the circle with centre O. If m(arc BC) = 110° and m(arc AB) = 125°, find measure arc AC.
AB is a diameter of a circle and AC is its chord such that ∠BAC = 30°. If the tangent at C intersects AB extended at D, then BC = BD.
In a right triangle ABC in which ∠B = 90°, a circle is drawn with AB as diameter intersecting the hypotenuse AC and P. Prove that the tangent to the circle at P bisects BC.
