Consider the following statements: 1) The number of circles that can be drawn through three non-collinear points is infinity. 2) Angle formed in minor segment of a circle is acute. Which of the above statements is/are correct?

Correct Answer: Neither 1 nor 2

Explanation:

Correct Answer: Both 1 and 2

Explanation:

Since it is an isosceles trapezium

So angle C = angle D = x

let A = 180 ?D = 180 ?x (since AB is parallel to CD)

B = 180-x

A+C = 180 ?x + x = 180 degrees (Property of cyclic quadrilateral)

ABCD is cyclic parallelogram with AB // CD and AD // BC

Considering angles A = C = y (Property of parallelogram) and B=D = x Also since it is cyclic A+C = B+D = 180 degrees

So x=y=90 degrees And also opposite sides are equal being a parallelogram

Thus ABCD is a rectangle

Correct Answer: 17 square feet

Explanation:

Correct Answer: 462 square cm

Correct Answer: Only one

Explanation:

let n-1, n, n+1 be 3 consecutive integers

So

(n+1)^2= n^2+ (n-1)^2

(n+1)^2-(n-1)^2= n^2

4n = n^2

So n = 0 or n = 4

n can?t be 0 as n-1 will be negative then

So 3,4 and 5 is the only triplet formed.

Correct Answer: 1, 2 and 3

Explanation:

AC-AB<BC Or AB+BC>AC

BC-AC<AB Or AB+AC>BC

AB-BC<AC Or AC+BC>AB

Sum of 2 sides of triangle is always greater than the third side

So all three statements are true

 

Correct Answer: 290

Correct Answer: 70

Correct Answer: 5?2

Correct Answer: (1 , 6)