International Maths Olympiad Forum By SOF Olympiad Trainer - Page 65

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Subject :IMO    Class : Class 5

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Class : Class 5
Its the option a

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Subject :IMO    Class : Class 3

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Subject :IMO    Class : Class 5

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Subject :IMO    Class : Class 9

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Subject :IMO    Class : Class 4

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Subject :IMO    Class : Class 5

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Subject :IMO    Class : Class 8

Ans 1:

Class : Class 8

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Subject :IMO    Class : Class 3

Anshul went to watch a show which started at quarter to six in the evening and ended at a quarter past 8. Anshul left the show 55 minutes before it ended and reach home at quarter to nine.
(A) At what time did Anshul leave the show?
(B) What was the duration of the show?
(C) How much time did he take to reach home?

(A) (B) (C)
A 7 : 25 p.m. 2 hours 15 minutes 1 hours 30 minutes
B 7 : 20 p.m. 2 hours 30 minutes 1 hours 25 minutes
C 7 : 10 p.m. 1 hours 15 minutes 2 hours 15 minutes
D 7 : 05 p.m. 1 hours 30 minutes 2 hours 25 minutes


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Class : Class 3

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Subject :IMO    Class : Class 5

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Subject :IMO    Class : Class 10

Let ABC be a right angled triangle in which AB = 3 cm, BC = 4 cm and ∠B = 90°. BD is the perpendicular from B on AC. The circle through B, C, D is drawn.
Given below are steps of construction of tangents from A to this circle. Identify the wrong step. Steps of construction :
Step I : Draw ΔABC and perpendicular BD from B on AC.
Step II : Draw a circle with BC as a diameter. This circle will pass through D.
Step III : Let O be the mid point of BC. Join AO.
Step IV : Draw a circle with AO as radius. This circle cuts the circle drawn in step II at B and P.
Step V : Join AP. AP and AB are desired tangents drawn from A to the circle passing through B, C and D.

AOnly I
BOnly IV
COnly III
DOnly V


AO should be the diameter, and not the radius, hence Step IV is incorrect.

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