Eighth graders from one of the schools decided to climb three castles in their hometown. Gathered in the school yard in the morning, the class was divided into three groups, the first group headed to Fortress A, located north of the school, the second group to Fortress B, located east of the school, and the third group to Fortress C, located northeast of the school. (See drawing)

School

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It is known that the first castle is 9 km away from the school, the second castle is 14 km away, and the third castle is 12 km away. Each group has a radio transmitter that catches within a radius of 10 km.

1) It is known that one hour later, group I had covered 4 km, group II had covered 4.5 km, and group III had covered 5 km,

Will groups 1 and 3 be able to communicate with each other by radio transmitter.

Will groups 1 and 2 be able to connect with each other at this time?

Will all three groups be able to connect with each other at this time?

2) It is known that after two hours the first and the second group covered an equal distance and the distance between them is 15 km, and the third covered 7.5 km in these two hours

What is the distance between groups I and III at this time?

What is the distance between groups III and II at this time?

What specific place does Group III occupy in the drawing at this time?

Will groups II and III be able to communicate with each other by radio at this time?

3) Find the distance between castles A and B if it is known that
4) Will the groups arriving at the destination be able to communicate with each other by radio?

5) How many meters should the radio transmitter be caught so that all three groups arriving at the destination can definitely connect with each other?