Advertisements
Advertisements
प्रश्न
If arcs AXB and CYD of a circle are congruent, find the ratio of AB and CD.
Advertisements
उत्तर
Let AXB and CYD are arcs of a circle whose centre and radius are O and r, respectively.
So, OA = OB = OC = OD = r ...(i)
∵ `bar(AXB) ≅ bar(CYD)`
∴ ∠AOB = ∠COD ...(ii) [Congruent arcs of a circle subtend equal angles at the centre]
In ΔAOB and ΔCOD,
AO = CO ...[From (i)]
BO = DO ...[From (i)]
∠AOB = ∠COD ...[From (ii)]
∴ ΔAOB ≅ ΔCOD ...[By SAS congruency]
`\implies` AB = CD ...[By C.P.C.T.]
`\implies (AB)/(CD) = 1`
Hence, the ratio of AB and CD is 1 : 1.
APPEARS IN
संबंधित प्रश्न
Fill in the blank:
Segment of a circle is the region between an arc and .................. of the circle.
Prove that the line joining the mid-point of a chord to the centre of the circle passes through the mid-point of the corresponding minor arc.
Prove that a diameter of a circle which bisects a chord of the circle also bisects the angle subtended by the chord at the centre of the circle.
If O is the centre of the circle, find the value of x in the following figures.
In the given figure, O and O' are centres of two circles intersecting at B and C. ACD is a straight line, find x.
In the given figure, if ∠ACB = 40°, ∠DPB = 120°, find ∠CBD.
In the given figure, two congruent circles with centres O and O' intersect at A and B. If ∠AOB = 50°, then find ∠APB.
If the given figure, AOC is a diameter of the circle and arc AXB = \[\frac{1}{2}\] arc BYC. Find ∠BOC.
In a circle, the major arc is 3 times the minor arc. The corresponding central angles and the degree measures of two arcs are
The chord of a circle is equal to its radius. The angle subtended by this chord at the minor arc of the circle is
