1957 AHSME Problems/Problem 47
Problem
In circle , the midpoint of radius is ; at , . The semi-circle with as diameter intersects in . Line intersects circle in , and line intersects circle in . Line is drawn. Then, if the radius of circle is , is:
Solution
Because is a diameter of the circle and , we know that bisects , so . Thus, is on the perpendicular bisector of , and so . Furthermore, by Thales' Theorem, . Thus, because is a right isosceles triangle with , it is a 45-45-90 triangle. Thus, . Now, draw and . Because is an inscribed angle which intercepts minor arc , the measure of central angle must be . Because , is also a -- triangle, so .
See Also
1957 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 46 |
Followed by Problem 48 | |
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