# Chord Properties of Circles

## Trending Questions

**Q.**

The perpendicular bisectors of the three sides of an acute triangle intersect each other

Inside the triangle

on the greatest side of the triangle.

outside the triangle

at any vertex of the triangle

**Q.**

Find the area of the minor segment of a circle of radius 14 cm, when its central angle is 60∘.Also find the area of the corresponding major segment. [Use π=227]

**Q.**

The perpendicular bisectors of three sides of an obtuse angled triangle intersect each other outside the triangle.

True

False

**Q.**

P is the centre of the circle . Prove that ∠XPZ=2(∠XZY+∠YXZ). [3 MARKS]

**Q.**

If a chord subtends an angle of 90∘^{ }at any point of the circumference of the circle. The name of the chord is

**Q.**

Find the equation of the circle which touches the x-axis at a distance of 3 from the origin and cuts an intercepts of 6 on the y-axis.

x2 + y2 − 6x − 6√2y + 9 = 0

x2 + y2 + 6x − 6√2y + 9 = 0

x2 + y2 − 6x − 6√2y + 9 = 0

x2 + y2 + 6x + 6√2y + 9 = 0

**Q.**In figure, two tangents RQ and RP are drawn from an external point R to the circle with centre O. If ∠PRQ=120∘, then prove that, OR=PR+RQ.

**Q.**

All the radii of a circle are$\_\_\_\_\_$.

**Q.**

Angle between the hour and minute hand of a clock at 11:15 is -

112.5∘

90∘

120∘

150∘

**Q.**

$PQ$ is a chord of the parabola which subtends a right angle at the vertex. Then locus of the centroid of triangle $PSQ$, where $S$ is the focus of a given parabola, is

**Q.**

In the given figure, a circle touches the side BC of △ABC at P and AB and AC produced at Q and R respectively. If AQ=15 cm, then the perimeter of △ABC is

**Q.**

If AB is a chord of a circle and P and Q are two points on the circle different from A and B, then:

The angle subtended by AB at P and Q are either equal or supplementary.

The sum of the angle subtended by AB at P and Q is always equal two right angle.

The angle subtended at P and Q by AB are always equal.

The sum of the angle subtended at P and Q is equal to four right angles

**Q.**

A chord of length 24 cm is at a distance of 5 cm from the centre of a circle. find the length of the chord of the same circle which is at a distance of 12 cm from the centre.

10 cm

15 cm

8 cm

13 cm

**Q.**When two straight lines are parallel their slopes are equal.

True

False

**Q.**Which of these pairs of lines are consistent?

- √3x−y=2;√6x−√2y=2
- x = 2; 2x - 7y - 5 = 0
- x3+y2=1;x+3y2=1
- 3y - 2x = 2; 2x - 3y = 2

**Q.**

A chord of a circle of radius 28 cm subtends a right angle at the center. What is the area of the minor sector?

**Q.**PQRS is a cyclic quadrilateral whose diagonals intersect at A. If ∠SQR=80∘ and ∠QPR=30∘, then find ∠SRQ.

- 80∘
- 70∘
- 60∘
- 50∘

**Q.**

The equation of the directrix of the parabola x2−4x−3y+10=0 is

y=−54

y=54

y=−34

x=54

**Q.**What is radius?

**Q.**

What will be the area of the largest square that can be cut out of a circle of radius $10\mathrm{cm}$?

$100{\mathrm{cm}}^{2}$

$200{\mathrm{cm}}^{2}$

$300{\mathrm{cm}}^{2}$

$400{\mathrm{cm}}^{2}$

**Q.**

Diameter is the longest chord of the circle.

- True
- False

**Q.**

The number of obtuse angles in the given figure is

a) 2

b) 3

c) 4

d) 5

**Q.**Question 7

The tangents to the circumcircle of an isosceles ΔABC at A, which AB=AC, is parallel to BC.

**Q.**

The figure shows two concentric circles with centre O. AB and APQ are tangents to the inner circle from point A lying on the outer circle. If AB = 7.5 cm then AQ is equal to:

12 cm

15 cm

18 cm

10 cm

**Q.**

In the given figure O is the centre of circle, ∠BAD = 75^{0} & chord BC = chord CD. Find ∠BOC, ∠OBD, ∠BCD.

75, 10, 105

75, 10, 115

75, 15, 115

75, 15, 105

80, 10, 105

80, 10, 115

80, 15, 105

80, 15, 115

**Q.**

In the figure, the pair of tangents AP and AQ, drawn from an external point A to a circle with centre O, are perpendicular to each other and length of each tangent is 4 cm, then the radius of the circle is

7.5 cm

4 cm

10 cm

2.5 cm

**Q.**

In the figure given, the radius of the circle is 15 cm. The angle subtended by the chord AB at the centre O is 60∘. What is the area of the minor segment?

- 20.4 cm2

- 200 cm2

- 40.8 cm2

- 40.4 cm2

**Q.**Prove that equal chords of a circle subtend equal angles at the centre

**Q.**Question 15

Two lines I and m intersect at the point O and P is a point on a line n passing through the point O such that P is equidistant from I and m. Prove that n is the bisector of the angle formed by I and m.

**Q.**

In a circle with centre O, chords AB and CD intersect inside the circumference at E. Prove that ∠AOC+∠BOD=2∠AEC.

[4 MARKS]