Circles Review – Fundamentals of Circles, Formulas for Circle, Congruent Circles, Tangent to a circle, Polygon inscribed in a Circle , Circle inscribed in a circle, Concentric Circles
Class Questions – Exercise 1 Exercise 2 Exercise 3 Exercise 4 Exercise 5
Practice Questions – Solutions
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Q.3
Circles C 1 with radius 7.25 and C 2 with radius 7.50 are concentric circles.
Quantity A Quantity B
The center of C 1 at (3, 3) The center of Circle C 2
A. If Quantity A is greater
B. If Quantity B is greater
C. If Quantity A and Quantity B are equal
D. The relationship cannot be determined from given information
Solution
Let us understand like this ;
There are two circles C 1 and C 2 .
Circles C1 and C2 are concentric circles that means both shares same center , so if center of circle C 1 is at the co-ordinates (3, 3) than the center of circle C2 will also be at co-ordinates ( 3, 3).
Hence correct answer choice is C.
Q.4
In the following figure diameter of the circle is 12.
Quantity A Quantity B
18.5 The area of triangle PQR
A. If Quantity A is greater
B. If Quantity B is greater
C. If Quantity A and Quantity B are equal
D. The relationship cannot be determined from given information
Solution:
To solve this type questions, always take care for the dimensions and data given related to question asked.
As per the information, figures are not drawn to the scale. There is not exact dimension and location of points P,Q and R of the triangle on the circle. Here lengths of sides of triangle or coordinates of points are also not given. In geometry, we cannot assume any data. The three points may lie on the circle with diameter 12 in following ways also.
Type A
In the above figure if we consider that PQ is equal to diameter of circle, which is 12 and take PR = PQ = Radius of circle than
area of triangle = 1/2 x b x h
= 1/2 x 6 x 6
= 18
Than Quantity A will be greater. Eliminate choice B and Choice C.
Type B:
Points P, Q and R lies on circle as following
In the above figure if we know one of the side either of PQ or QR , the area of the triangle will be lesser than Type A.
Here every time we will get the different area of the triangle. Hence, the area of triangle PQR cannot be determined from the information given,
so the answer will be D.