In the peaceful environment of a garden, where the mind can rest and focus, a simple yet intriguing geometric puzzle awaits. Consider two semicircles placed side by side, centered at points O and Q. The semicircles have collinear diameters AB and BC, where AB is shorter than BC.
Radii OD and QE, drawn perpendicular to the line AC, give us the points D and E. A segment connecting D and E intersects the arc BE at F, which is the midpoint of DE. With the distance from point O to point B being one unit, your task is to calculate the length of BQ.
This problem not only helps sharpen your spatial reasoning but also offers a chance to clear your mind, similar to how gardening exercises help in improving mental health. Engage with the problem, find the solution, and see how such mental challenges can enhance focus, clarity,
and cognitive agility—whether you're in a garden or a study space!
Two semicircles centered at O and Q have collinear diameters AB and BC, with AB shorter than BC. Radii OD and QE are perpendicular to AC. Segment DE intersects arc BE at F, the midpoint of DE. Given OB equals 1 unit, find BQ.
Circles touch the sky,
radii stand tall and true,
logic finds its path.
Geometry Problems
Open Problems
Visual Index
All
Problems
Triangle
Circle
Diameter
Circular Sector
Semicircle
Midpoint
Secant line
Parallel lines
Perpendicular lines
Angle
45-Degree Angles
Congruence
Right Triangle
Special Right Triangle
Quadrilaterals
Trapezoid
Cyclic Quadrilateral
View or Post a solution