Advertisements
Advertisements
प्रश्न
In the following figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to ______.
विकल्प
2 cm
3 cm
4 cm
5 cm
Advertisements
उत्तर
In the following figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to 2 cm.
Explanation:
We know that, the perpendicular from the centre of a circle to a chord bisects the chord.
AC = CB = `1/2` AB = `1/2` × 8 = 4 cm
Given OA = 5 cm
AO2 = AC2 + OC2
(5)2 = (4)2 + OC2
25 = 16 + OC2
OC2 = 25 – 16 = 9
OC = 3 cm ...[Taking positive square root, because length is always positive]
OA = OD ...[Same radius of a circle]
OD = 5 cm
CD = OD – OC
= 5 – 3
= 2 cm
APPEARS IN
संबंधित प्रश्न
In Figure 1, common tangents AB and CD to the two circles with centres 01and 02 intersect at E. Prove that AB = CD.
In the given figure, PQ is a chord of length 8cm of a circle of radius 5cm. The tangents at P and Q intersect at a point T. Find the length TP
Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠PTQ = 2∠OPQ.
ABCD is a quadrilateral such that ∠D = 90°. A circle (O, r) touches the sides AB, BC, CD and DA at P,Q,R and If BC = 38 cm, CD = 25 cm and BP = 27 cm, find r.
In the given figure, the chord AB of the larger of the two concentric circles, with center O, touches the smaller circle at C. Prove that AC = CB.
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, OQ : PQ = 3.4 and perimeter of Δ POQ = 60 cm. Determine PQ, QR and OP.
In the given figure, O is the centre of a circle, chord PQ ≅ chord RS If ∠ POR = 70° and (arc RS) = 80°, find –
(1) m(arc PR)
(2) m(arc QS)
(3) m(arc QSR)
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.
If AB = 12 cm, BC = 16 cm and AB is perpendicular to BC, then the radius of the circle passing through the points A, B and C is ______.
