Hole-Circle Coordinates: Radius, Axes and a Supplied Direction

Hole-Circle Coordinates: Radius, Axes and a Supplied Direction

Original quantitative learning practice in English. All 24 questions are included. Four supplied cases exercise six related calculation targets; they form one topic, not four separate tests. Every question includes the complete initial data. Use the stated model and retain intermediate precision. Choose one answer. Learning target: 20/24, not an official pass mark. This bank covers the calculation topic in its title; it is not a complete professional examination, design approval or operating instruction.
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A four-hole pattern has circle diameter 120 mm and centre (160,130) mm. Three holes lie in the right, upper and left cardinal directions. A separate test point on the same circle has direction cosines x=0.6 and y=0.8; their squared sum is one. All coordinates refer to hole centres. Calculate the circle radius in mm. Keep intermediate values unrounded; round the final result to four decimal places if necessary.