Chord of the Bigger Circle Is Bisected at the Point of Contact with the Smaller Circle

Q. Question 6
If two chord AB and CD of a circle AYDZBWCX intersect at right angles, then prove that arc CXA + arc DZB = arc AYD + arc BWC = semi-circle.

Q. Question 7
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.

Q. In the given figure, two concentric circles are drawn. If the radius of an inner circle = 3 cm and the length of the chord of an outer circle which touches an inner circle = 8 cm then, find the radius of an outer circle.

1. 7 cm
2. 6 cm
3. 5 cm
4. 10 cm

Q.

A tangent $PQ$ at a point $P$ of a circle of radius $5cm$ meets a line through the centre $O$ at a point $Q$ so that $OQ=12cm$. Length $PQ$ is :

1. $12cm$

2. $13cm$

3. $8.5cm$

4. $\sqrt{119}cm$

Q. In the given figure, circles with centres C and D touch internally at point E. D lies on the inner circle. Chord EB of the outer circle intersects inner circle at point A. Prove that, seg EA ≅ seg AB.

Q.

Question 1
If Radii of two concentric circles are 4 cm and 5 cm, then length of each chord of one circle which is tangent to the other circle, is
(A) 3 cm
(B) 6 cm
(C) 9 cm
(D) 1 cm

Q. A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered in the water and its size is such that when it touches the sides, it is just immersed. What fraction of the water overflows? [4 MARKS]

Q. Two concentric circles are of radii 5 cm and 3 cm, respectively. Find the length of the chord of the larger circle that touches the smaller circle.

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.

Q. For the given concentric circles with radius 5 cm and 13 cm respectively. Find the length of the chord AB.

Q. If $PAB$ is a secant to a circle of centre $O$ intersecting the circle of $A$ and $B$ and $PT$ is tangent segment, then prove that-
$PA\times PB=P{T}^2$

Q. Question 1
Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8cm is a tangent to the inner circle, . Find the radius of the inner circle.

Q. In the given figure there are two concentric circles. PQ is a chord of the outer circle which touches the inner circle at point L. Select the correct option from the following.

1. PL > QL
2. PL = QL
3. PL < QL
4. PL = 2 $\times$ QL

Q. Assertion (A)
In the given figyre, a quadrilateral ABCD is drawn to circumscribe a given circle, as shown.
Then, AB + BC = AD + DC.
Figure

Reason (R)
In two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R)is true.

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

1. 10 cm
2. 8 cm
3. 4 cm
4. 12 cm

Q. Two concentric circles are of radii 5 cm and 3 cm, respectively. Find the length of the chord of the larger circle that touches the smaller circle.

Q. Question 1
Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8cm is a tangent to the inner circle, . Find the radius of the inner circle.

Q. For two concentric circles, if AB is a chord of the outer circle touching the inner circle at point P, then PB = $\frac{AB}{2}$

1. True
2. False

Q. Which of the following is correct about two concentric circles?

1. Concentric circles have 2 common tangents.
2. None of the above
3. The inner circle has a radius greater than the radius of the outer circle.
4. Concentric circles cannot have common tangents.

Q.

Two circles of radii 5 cm and 3 cm are concentric. Calculate the length of a chord of the outer circle which touches the inner circle.

1. 12 cm

2. 2 cm

3. 8 cm

4. 23 cm

Q. For the given concentric circles with radius 5 cm and 13 cm respectively. The length of the chord AB =

1. 24 cm
2. 16 cm
3. 12 cm

Q.

Two circles of radii 5 cm and 3 cm are concentric. Calculate the length of a chord of the outer circle which touches the inner circle.

1. 12 cm

2. 2 cm

3. 8 cm

4. 23 cm

Q. In the given figure, two concentric circles are drawn. If the radius of an outer circle = 13 cm and the length of the chord of an outer circle which touches an inner circle = 24 cm then, find the radius of inner circle.

1. 5 cm
2. 4 cm
3. 6 cm
4. 5.5 cm