## Wednesday, 5 October 2011

### Geometry Concept Problems-2 (Circle)

Related Concepts:-
Length of arc = (angle made by the arc at the centre) * (2πr) / 3600
Area of circular region covered under arc
= (angle made by the arc at the centre) * (πr2) / 3600
Circumference of the circle = 2πr
(This is the arc length for complete 3600 angle made at the centre)
ÐAOB = ÐCOD                 ÐAOC = ÐBOD
Length of arc AB = length of arc CD
Length of arc AC = length of arc BD

The possible quant-comparison Q’s in GRE:
Each question from Q1 to Q5 consists of two quantities, one in column A and one in column B. You are to compare the two quantities and choose
A if the quantity in column A is greater;
B if the quantity in column B is greater;
C if the quantities are equal;
B if the relationship cannot be determined from the information given;

Q1)         Column A                                                            Column B
Length of arc AB                                               Length of arc CD

Q2)         Column A                                                            Column B
Length of arc AC                                               Length of arc BD

Q3) Given that ÐAOB is acute angle
Column A                                                            Column B
Length of arc AB                                               Length of arc BD

Q4)         Column A                                                            Column B

Q5)           Column A                                                            Column B

The possible problem-solving Q’s in GRE/GMAT:
Q6) If the ÐAOB = 600 and radius of the circle is 4 units, find the length of arc AB

Q7) If the ÐAOB = 600 and the radius of the circle is 3 units, find the total area of shaded region

Q8) If a straight-line is drawn joining A and B and given that the ÐAOB = 600 and
radius measures 3 units, find the length of the straight-line AB

Q9) If length of arc ACDB is double that of arc AB, then find ÐAOB

Note:-
Please find the solutions to these problems in the next post on this blog.