Theorem 2: Perpendicular from the Center to a Chord Bisects the Chord
Trending Questions
The circle inscribed in an equilateral triangle of sides 24 cm just touches the sides of the triangle. Find the area of the rest part of the triangle (let √3=1.732)
93 sq.cm
98.54 sq.cm
92.70 sq.cm
96.67 sq.cm
Two circles of radii 4 cm and 3 cm intersect at two points and the distance between their centres is 5 cm. Find the length of the common chord.
4.8 cm
2.8 cm
7 cm
5.5 cm
In the given figure, O is the centre of the circle. Find x.
50∘
40∘
20∘
30∘
In figure A, B, C are three points on a circle such that the angles subtended by the chord AB and AC at the centre O are 80∘and 120∘ respectively. Determine ∠BAC and the degree measure of arc BPC.
Equal chords AB and CD of a circle with centre O, cut at right angles at E. If M and N are the mid - points of AB and CD respectively, then OMEN is a
- 30∘
- 60∘
- 90∘
- 45∘
Two circles of radii 5 cm and 6 cm with common centre are drawn. There is a line AB such that it is chord to both the circles. CD=8 cm. Find the distance of the chord from centre and the length of AC respectively.
3 cm, 1.19 cm
2.55 cm, 2.35 cm
3 cm, 2 cm
2.16 cm, 2.35 cm
- 60∘
- 30∘
- 45∘
- 15∘
In the figure, O is the centre of the circle. If ∠BAC=52∘, then ∠OCB is equal to
52
104
38
76
If two arcs of equal length subtend angles x and y at the centre, then x = __
y
2y
5y
3y
AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24 cm. If the chords are on opposite sides of the centre and the distance between them is 17 cm, find the radius of the circle.
13 cm
10 cm
11 cm
12 cm
In two concentric circles with centre O, if AD is the chord of the larger circle, then AB = CD.
True
False
- 120o
- 240o
- 60o
- 30o
In the figure, if ∠OAB=40∘, the ∠ACB is equal to
(A) 50∘
(B) 40∘
(C) 60∘
(D) 70∘
- 100∘
- 110∘
- 120∘
- 130∘
If two equal chords AB and CD of a circle when produced, intersect at point P, then PB =
PD
CY
None of the above
DY
The length of arc AB is twice the length of arc BC of a circle with centre O. If ∠AOB is 100o then ∠BOC is
50o
60o
70o
55o
A chord AB of a circle whose centre is O, is bisected at E by a diameter CD. OC= OD = 15 cm and OE = 9 cm. Find the length of AD.
60°
70°
80°
90°
In the given figure ∠ AOC=130∘, The value of ∠ ABC (in degrees) is _______.
115∘
50∘
100∘
95∘
It is possible for two chords to not be equal even if they are at a same distance from the centre when
the chords are parallel to each other
the chords are perpendicular to each other
the chords are drawn to concentric circles
None of these
- 45°
- 30°
- 15°
- 60°
The perpendicular to a chord from the centre of the circle divides the chord in ratio of
1:1
1:3
1:2
1:4
- 80°
- 90°
- 75°
- 85°
Check whether the following statement is true or false:
If AB and AC are two chords of a circle with centre O, then we can conclude that ∠AOB=∠AOC.
- t1+t2=0
- t1(t1+t2)+2=0
- t1t2=−1
- None of these
S1: AM=AP2, BN=BP2
S2: OO′=AM+BN
Choose the correct option.
Only S1 is true.
S1 is true & S2 is false.
Both statements are true.
Only S2 is true.