CBSE Class 10 Mathematics Circles VBQs Set A

CBSE Class 10 Mathematics Circles VBQs Set A

CIRCLE

1. There are 3 villages A, B and C such that the distance from A to B is 7 km, from B to C is 5 km and from C to A is 8 km. The gram pradhan wants to dig a well in such a way that the distance from each villages are equal. What should be the location of well? Which value is depicted by gram pradhan?

2. People of village wants to construct a road nearest to a circular village Rampur. The road cannot pass through the village. But the people wants that road should be at the shortest distance from the center of the village (i) which road will be the nearest to the center of village? (ii) which value is depicted by the people of village?

3. Four roads have to be constructed by touching village Khanpur in circular shape of radius 1700 m in the following manner.

Savita got contract to construct the roads AB and CD while Vijay got contract to construct AD and BC.

Prove that AB + CD = AD + BC. Which value is depicted by the contractor?

4. Two roads starting from P are touching a circular path at A and B.

Sarita ran from P to A 10 km and Ramesh ran from P to B. (i) If Sarita wins the race than how much distance Ramesh ran? (ii) Which value is depicted?

5. A farmer wants to divide a sugarcane of 7 ft length between his son and daughter equally. Divide it Geometrically, considering sugarcane as a line of 7cm, using construction.

(i) Find the length of each part.

(ii) Which value is depicted?

ASSERTION AND REASONING BASED QUESTION

Question : Assertion (A): PA and PB are two tangents to a circle with centre O. Such that ∠AOB = 1100, then ∠APB = 900.
Reason (R): The length of two tangents drawn from an external point are equal.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : D

Question : Assertion (A): If in a circle, the radius of the circle is 3 cm and distance of a point from the centre of a circle is 5 cm, then length of the tangent will be 4 cm.
Reason (R): (hypotenuse) 2 = (base) 2 + (height) 2
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : A

Question : Assertion (A): If a chord AB subtends an angle of 600 at the centre of a circle, then the angle between the tangents at A and B is also 600.
Reason (R): The length of the tangent from an external points P on a circle with centre O is always less than OP.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : D

Question : Assertion (A): The two tangents are drawn to a circle from an external point, then they subtend equal angles at the centre.
Reason (R):A parallelogram circumscribing a circle is a rhombus.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : B

Question : Assertion (A): The length of the tangent drawn from a point 8cm away from the centre of circle of radius 6cm is 2√7 cm.
Reason (R): If the angle between two radii of a circle is 1300, then the angle between the tangents at the end points of radii at their point of intersection is 500.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : B