# Theorem of Equal Chords Subtending Angles at the Center

## Trending Questions

**Q.**

If AB, BC, and CD are equal chords of a circle with O as center, and AD diameter then ∠AOB equals to

None of these

60∘

90∘

120∘

**Q.**

The radius of a circle is 8 cm and the length of one of its chords is 12 cm. Find the distance of the chord from the centre.

**Q.**If chords AB and CD of congruent circles subtend equal angles at their centres, then which of the option is correct?

AB=CD

AB>CD

AB<CD

None of the above

**Q.**

In the adjoining figure, DE is a chord parallel to diameter AC of the circle with centre O. If ∠CBD=60∘, calculate ∠CDE.

**Q.**Seg PM and seg PN are congruent chords of a circle with centre C. Show that the ray PC is the bisector of $\angle $NPM.

**Q.**

In the given figure ∠ AOC=130∘, The value of ∠ ABC (in degrees) is _______.

- 115
- 50
- 100
95

**Q.**

In the figure, AB is a diameter of a circle with centre O and CD. If ∠BAC = 20∘, find the values of (i)∠BOC (ii)∠DOC (iii)∠DAC (iv)∠ADC

**Q.**

Question 6

Salil wants to put a picture in a frame. The picture is 735cm wide. To fit in the frame the picture cannot be more than 7310cm wide. How much should the picture be trimmed?

**Q.**In figure ABCD is a cyclic quadrilateral; O is the centre of the circle. If ∠BOD=160∘, find the measure of ∠BPD , as shown in the given figure.

**Q.**

In the given figure, O is the centre of a circle in which chords AB and CD intersect at P such that PO bisects ∠BPD. Prove that AB = CD.

**Q.**

If the angles subtended by the chords of a circle at the centre are equal, then the chords are

Not equal to each other

Parallel to each other

Equal to each other

Perpendicular to each other

**Q.**

A sector of a circle with a radius $18\mathrm{cm}$ has a central angle $120\xb0$. Find the area of the sector. Use $\mathrm{\pi}=3.14$

**Q.**In the given figure, ABC is isosceles triangle with AB=AC, ∠BCD=20∘. The measure of ∠ACB is equal to

100∘

80∘

60∘

70∘

**Q.**

If two chords of a circle are equal, then their corresponding arcs will be equal.

False

- True

**Q.**

Which statements are true regarding the area of circles and sectors? Check all that apply.

The area of a circle depends on the length of the radius.

The area of a sector depends on the ratio of the central angle to the entire circle.

The area of a sector depends on $\mathrm{\pi}$.

The area of the entire circle can be used to find the area of a sector.

The area of a sector can be used to find the area of a circle.

**Q.**

In figure, A, B, and C are three points on a circle with centre O such that ∠BOC = 300 and ∠AOB = 600. If D is a point on the circle other than the arc ABC, find ∠ADC (in degrees).

**Q.**

The minute hand of a circular clock is $15cm$ long. How far does the tip of the minute hand move in $1$ hour. (Take $\mathrm{\pi}=3.14$)

**Q.**

Show that the tangents at the end points of a diameter of a circle are parallel.

**Q.**In the given figure, O is the centre of the circle of radius 10 cm. AB and AC are two chords such that

AB=AC=4√5 cm.

The length of chord BC is

12.4 cm

24 cm

8 cm

16 cm

**Q.**If AB=CD and ∠AOB=50∘, then ∠ODC = _____ .

- 65∘
- 50∘
- 75∘
- 85∘

**Q.**

Equal chords subtend equal angles at the centre.

- True
- False

**Q.**

**Question 2**

A chord AB of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the major arc and also at a point on the minor arc.

**Q.**

In the following figure, what can be concluded from the below given conditions.

Given: AB = CD and AC = DE.

All of the above.

AC = BD, ∠AOC = ∠BOD

∠AOC = ∠DOE, AC = DE

AD = CE, ∠AOD = ∠COE.

**Q.**In the figure, AOB is a diameter of the circle and C, D, E are any three points on the semi-circle. Find the value of ∠ACD+∠BED.

**Q.**AB and PQ are two equal chords of a circle. If the length of minor arc and major arc formed by AB is 24cm and 64cm, respectively, then find the length of minor and major arc formed by PQ.

**Q.**

Two circles of radius 3 cm and 5cm have a common centre, O. AB is a chord to both the circles and length of CD is 2√5 cm. Find the distance of the chord from the centre and the length AC.

**Q.**In the figure, ∠ADC=130∘ and chord BC = chord BE. Find ∠CBE

**Q.**

Two circles of radius 3 cm and 5cm have a common centre, O. AB is a chord to both the circles and length of CD is 2√5 cm. Find the distance of the chord from the centre and the length AC.

**Q.**A chord of length 6 cm is drawn on a circle of radius 5 cm. Calculate its distance from the centre of the circle.

**Q.**Find the value of x in the given figure if∠AOB=70° and AB = CD.

- 70°
- 80°
- 50°
- 60°