Perpendicular from the Center to a Chord Bisects the Chord

Q.

Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

1. 6 cm

2. 12 cm

3. 8 cm

4. 10 cm

Q. Question 5
Two circles with centers O and O’ of radii 3 cm and 4 cm , respectively intersect at two points P and Q, such that OP and O’P are tangents to the two circles. Find the length of the common chord PQ.

Q.

In the given figure, O is the centre of two concentric circles of radii 6 cm and 10 cm. AB is a chord of outer circle which touches the inner circle. The length of chord AB is

(a) 8 cm (b) 14 cm (c) 16 cm (d) $\sqrt{136}$ cm

Q.

A chord in a circle of radius 15 cm subtends an angle of 60${}^{\circ }$ at the centre. Find the areas in $c{m}^2$ of the corresponding minor and major segments of the circle.(Use $\pi$ = 3.14 and $\sqrt{3}$ = 1.73)

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.

1. 2 cm

2. 4 cm

3. 5 cm

4. 7 cm

Q. Two concentric circles are of radii 6.5 cm and 2.5 cm. Find the length of the chord of the larger circle which touches the smaller circle [CBSE 2011]

Q.

In a circle of radius 17 cm, two parallel chords of lengths 30 cm and 16 cm are drawn. Select the statements that are true.

1. Distance between the chords if both the chords are on the opposite sides of the centre is 23 cm.

2. Distance between the chords if both the chords are on the same side of the centre is 7 cm.

3. Distance between the chords if both the chords are on the opposite sides of the centre is 28 cm.

4. Distance between the chords if both the chords are on the same side of the centre is 17 cm.

Q.

PQ is a chord of length 4.8 cm of a circle of radius 3 cm. The tangent at P and Q intersect at a point T as shown in the figure. Find the length of TP.

Q.

A chord of length 8 cm is drawn at a distance of 3 cm from the centre of a circle. Calculate the radius of the circle.

1. 5 cm

2. 8 cm

3. 4 cm

4. 9 cm

Q.

Prove that a diameter $AB$ of a circle bisects all those chords which are parallel to the tangent at the point $B.$

Q.

In two concentric circles, a chord of length 8 cm of the larger circle touches the smaller circle. If the radius of the larger circle is 5 cm then find the radius of the smaller circle.

Q. Two concentric circles of radii 3 cm and 5 cm are given. Then length of chord BC which touches the inner circle at P is equal to

(a) 4 cm

(b) 6 cm

(c) 8 cm

(d) 10 cm

Q.

Two concentric circles are of radii 25 cm and 24 cm .The length of the chord of the larger circle which touches the smaller circle is

1. 14 cm

2. 28 cm

3. 21 cm

4. 7 cm

Q. 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. [CBSE 2014]

Q. A chord PQ of length 12 cm subtends an angle of 120° at the centre of a circle. Find the area of the minor segment cut off by the chord PQ.

Q. In the given figure, in a circle with centre O, length of chord AB is equal to the radius of the circle. Find measure of each of the following.
(1) ∠ AOB (2)∠ ACB
(3) arc AB (4) arc ACB.

Q.

In the given figure, the chord AB of the larget of the two concentric circles, with centre O, touches the smaller circle at C. Prove that AC = CB.

Q.

The radius of a circle is 17.0 cm and the length of perpendicular drawn from its centre to a chord is 8.0 cm. Calculate the length of the chord.

1. 20 cm

2. 5 cm

3. 10 cm

4. 30 cm

Q. In the given figure, the chord AB of the larger of the two concentric circles, with centre O, touches the smaller circle at C. Prove that AC = CB.

Q.

In the given figure, O is the centre of the circle with radius 5 cm. OP and OQ are perpendiculars to AB and CD respectively. AB = 8 cm and CD = 6 cm. Determine the length of PQ.

Q. Question 4
A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding: (i) minor segment (ii) major sector. $(Use\pi =3.14)$

Q. If $d_1,d_2(d_2>d_1)$ be the diameters of two concentric circle s and c be the length of a chord of a circle which is tangent to the other circle , prove that ${d_2}^2=c^2+{d_1}^2$.

Q. Question 2
In figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to

(A) 2 cm
(B) 3 cm
(C) 4 cm
(D) 5 cm

Q.

In the diagram a semicircle is drawn at one side of an equilateral triangle. If BC is 12 cm, what is the radius of the semicircle?

1. 6

2. 3

3. 12

4. 9

Q. In the given figure, PQ is a chord of a circle with centre O and PT is a tangent. If ∠QPT = 60^∘ , find ∠PRQ

Q.

Prove that in any circle, the tangents at two points make equal angles with the chord joining the points of contact.

Q. Two parallel chords are drawn on either side of the centre of a circle of diameter 30 cm. If the length of one chord is 24 cm and the distance between the two chords is 21 cm, then find the length of another chord.
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Q. In the given figure, circles with centres X and Y touch internally at point Z . Seg BZ is a chord of bigger circle and it itersects smaller circle at point A. Prove that, seg AX || seg BY.

Q.

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

1. 10 cm

2. 13 cm

3. 5 cm

4. 21 cm

Q. In the given figure, two circles intersect each other at points A and E. Their common secant through E intersects the circles at points B and D. The tangents of the circles at points B and D intersect each other at point C. Prove that ▢ABCD is cyclic.