Advertisements
Advertisements
प्रश्न
Length of a chord of a circle is 24 cm. If distance of the chord from the centre is 5 cm, then the radius of that circle is ______.
पर्याय
12 cm
13 cm
14 cm
15 cm
उत्तर
Length of a chord of a circle is 24 cm. If distance of the chord from the centre is 5 cm, then the radius of that circle is 13 cm.
Explanation:
Let the chord be AB = 24 cm
Distance of the chord from the centre O is 5 cm.
AO is the radius of the circle.
Perpendicular from the centre of the circle to the chord bisects the chord.
So, AC = CB
In ΔAOC,
OC2 + AC2 = AO2
⇒ 52 + 122 = AO2
⇒ AO2 = 25 + 144
⇒ AO2 = 169
⇒ AO = 13 cm
Thus, the radius of the circle is 13 cm.
APPEARS IN
संबंधित प्रश्न
Tangents PA and PB are drawn from an external point P to two concentric circles with centre O and radii 8 cm and 5 cm respectively, as shown in Fig. 3. If AP = 15 cm, then find the length of BP.
A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC ?
In the given figure, if ∠BAC = 60° and ∠BCA = 20°, find ∠ADC.
Two concentric circles are of diameters 30 cm and 18 cm. Find the length of the chord of the larger circle which touches the smaller circle.
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 figure, seg MN is a chord of a circle with centre O. MN = 25, L is a point on chord MN such that ML = 9 and d(O,L) = 5. Find the radius of the circle.
Draw a circle of radius 4.8 cm and mark its center as P.
(i) Draw radii PA and PB such that ∠APB = 45°.
(ii) Shade the major sector of the circle
The ______________ is the longest chord of a circle
The length of tangent from an external point on a circle is always greater than the radius of the circle.
A quadrilateral ABCD is inscribed in a circle such that AB is a diameter and ∠ADC = 130º. Find ∠BAC.
