Geometry Previous Year Questions (CAT)  Set 0003

Previous years`s CAT questions: Geometry
Post your solutions as reply to respective questions below.

Question 1
A ladder leans against a vertical wall. The top of the ladder is 8m above the ground. When the bottom of the ladder is moved 2m farther away from the wall, the top of the ladder rests against the foot of the wall. What is the length of the ladder?
1. 10m
2. 15m
3. 20m
4. 17m (CAT 2001)

Answer: Option 4

Question 2
In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm and 9 cm respectively. Let D be a point on the line segment BC such that AD is perpendicular to BC. If AD = 3 cm, then what is the radius (in cm) of the circle circumscribing the triangle ABC?
1) 17.05
2) 27.85
3) 22.45
4) 32.25
5) 26.25 (CAT 2008 )

Answer: Option 5

Question 3
Consider a square ABCD with midpoints E, F, G, H of AB, BC, CD and DA respectively. Let L denote the line passing through F and H. Consider points P and Q, on L and inside ABCD, such that the angles APD and BQC both equal 120Â°. What is the ratio of the area of ABQCDP to the remaining area inside ABCD?
(CAT 2008 )

Answer: Option 5

Question 4
(CAT 2008 )

Answer: Option 5

Question 5
(CAT 2008 )

Answer: Option 1

Question 6
Two identical circles intersect so that their centres, and the points at which they intersect, form a square of side 1 cm. The area in sq. cm of the portion that is common to the two circles is
(CAT 2005)

Answer: Option 2

Question 7
In the following figure, the diameter of the circle is 3 cm. AB and MN are two diameters such that MN is perpendicular to AB. In addition, CG is perpendicular to AB such that AE : EB = 1 : 2, and DF is perpendicular to MN such that NL : LM = 1 : 2. The length of DH in cm is
(CAT 2005)

Answer: Option 2

Question 8
Consider the triangle ABC shown in the following figure where BC = 12 cm, DB = 9 cm, CD = 6 cm and ∠BCD = ∠BAC. What is the ratio of the perimeter of the triangle ADC to that of the triangle BDC ?
(1) 7/9 (2) 8/9 (3) 6/9 (4) 5/9 (CAT 2005)

Answer: Option 1

Question 9
(CAT 2005)

Answer: Option 1

Question 10
(CAT 2004)