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# Geometry eLitmus Questions, Geometry Questions for eLitmus pH Test

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 1 What is the minimum number of distinct lines representing the altitudes,medians,and interior angles bisector of an obtuse triangle ? A. 5 B. 6 C. 7 D. 9
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Explanation

Consider an isosceles obtuse angle triangle.

Median, Altitude and Angle bisectors will be as shown in the diagram below.

As clear from the above three figure, one line is common for all the above(line passing from obtuse angle vertex)

So the minimum number of lines required is: 7.

 2 There is a circular track of 440 meters. There are three persons Symonds, Harbhajan and Inzmam standing on different points on the track ready to start the race. Symonds and Harbhajan are standing diametrically opposite to each other while Inzmam is midway between them such that Symonds, Inzmam and Harbhajan are standing in clockwise direction. The race started at 10 AM. The speed of Symonds, Harbhajan and Inzmam are respectively 5 m/s, 10 m/s and 8 m/s. At what time would Harbhajan and Inzmam meet for the second time if all of three run in clockwise direction ? A. 10:06:25 AM B. 10:04:35 AM C. 10:03:50 AM D. None of these
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 3 The interior angles of an octagon ABCDEFGH are in AP. If the largest and the second largest have an average of x is 1520. Find the average of the least two ? A. 117 B. 131 C. 141 D. None of these
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Explanation

Suppose the angles are: a, a+d, a+2d, a+3d, a+4d, a+5d, a+6d, a+7d

Given that: (a+6d + a+7d)/2 = 1530

=> 2a + 13d = 306       -------- (1)

We know that sum of all interior angles of a polygon of n sides is: (n-2)*180

So, a + a+d + a+2d + a+3d + a+4d + a+5d + a+6d + a+7d = (8-2)*180

=> 8a + 28d = 1080

=> 2a + 7d = 270         -------- (2)

(1) - (2) gives: 6d = 36

so, d = 6

Solving from (1) we get a = 114

So, the smallest = 114

second smallest angle = 114 + 6 = 120

So average of first two smallest is: (114 + 120)/2 = 117

 4 Two circles with centres P and Q cut each other at two distinct points A and B. The circles have the same radii and neither P nor Q falls within the intersection of the circles. What is the smallest range that includes all possible values of the angle AQP in degrees? A. Between 0 and 90 B. Between 0 and 30 C. Between 0 and 60 D. Between 0 and 75 E. Between 0 and 45
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 5 ABCD is a rectangle with AD being longer side.P and Q be the mid-points of AB and CD.x is a point on AD.Then what is the ratio of Area of PQCB to XCB? A. 1:1 B. 1:2 C. 1:3 D. 1:4
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Explanation

Area of rectangle formed by PQCB is PQ*CQ
Area of triangle formed by XCB is (1/2)BC*AB