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?
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
In the given figure, tangents PQ and PR are drawn from an external point P to a circle with centre O, such that ∠RPQ = 30°. A chord RS is drawn parallel to the tangent PQ. Find ∠RQS.
In the given figure, PA and PB are the tangent segemtns to a circle with centre O. Show that he points A, O, B and P are concyclic.
In the given figure, an isosceles triangle ABC, with AB = AC, circumscribes a circle. Prove that point of contact P bisects the base BC.
In the given figure, O is the centre of the two concentric circles of radii 4 cm and 6cm respectively. AP and PB are tangents to the outer and inner circle respectively. If PA = 10cm, find the length of PB up to one place of the decimal.
In Fig., chords AB and CD of the circle intersect at O. AO = 5 cm, BO = 3 cm and CO = 2.5 cm. Determine the length of DO.
Use the figure given below to fill in the blank:
________ is a radius of the circle.
The center of a circle is at point O and its radius is 8 cm. State the position of a point P (point P may lie inside the circle, on the circumference of the circle, or outside the circle), when:
(a) OP = 10.6 cm
(b) OP = 6.8 cm
(c) OP = 8 cm
In the figure, O is the centre of a circle, AB is a chord, and AT is the tangent at A. If ∠AOB = 100°, then ∠BAT is equal to ______
In the adjoining figure ‘O’ is the center of the circle, ∠CAO = 25° and ∠CBO = 35°. What is the value of ∠AOB?
Find the length of the arc of a circle which subtends an angle of 60° at the centre of the circle of radius 42 cm.
