GRE-Style: Inscribed Shapes

GRE Quantitative · Axiom Academy

EXAMPLE GRE-Style: Inscribed Shapes Spotting the ONE shared measurement that links an inscribed square to its circle A square is inscribed in a circle of radius 5 . What is the area of the square? Nice work — you found the ONE shared measurement that connects an inscribed square to its circle, and used it to get the area without ever drawing a coordinate grid. The key relationship: a square inscribed in a circle always has diagonal = diameter of the circle. Spotting that single fact is the whole problem. From diagonal to side: a square's diagonal and side are related by , so . Result: with r = 5 , the diagonal is 10 , the side is , and the area is . This generalizes: GRE "shape inscribed in shape" problems almost always hinge on ONE shared measurement — a diagonal, a radius, or a shared side — that ties the two shapes together. Find that link first, then the rest is algebra.

This is the written version of the interactive lesson above. See the full GRE Quantitative course.