Mathematics & Logic

Tackle Fierce Geometric Proof Challenges

Delve into ten expert-level puzzles fusing logic and geometry for ultimate mental sharpening.

#trigonometric geometry#conic sections#geometry proofs#coordinate loci#polyhedral relations#cyclic properties#power of point#concurrency conditions#spatial deduction#Euclidean theorems

Quiz Intelligence

Total Questions

Difficulty Level

hard

Progress

0/0

Quiz Questions

Answer all questions below and test your knowledge.

1
In triangle ABC, cevians AD, BE, CF meet at a point. Ceva's theorem states:
Question 1
2
For point P outside circle center O, secant PAB intersecting at A and B, tangent PT:
Question 2
3
Ptolemy's theorem for cyclic quadrilateral ABCD asserts:
Question 3
4
Euler's formula for convex polyhedra relates vertices V, edges E, faces F as:
Question 4
5
The orthocenter, centroid, circumcenter of an acute triangle are collinear on:
Question 5
6
In coordinate plane, circle equation through (1,2), (3,4), (-1,0) has center at:
Question 6
7
For vectors u, v with dot product u·v = |u||v|cosθ, right angle between them when:
Question 7
8
Nine-point circle passes through midpoints of sides, feet of altitudes, and:
Question 8
9
Inradius r of equilateral triangle side a equals:
Question 9
10
For parabola y²=4ax, focus is at:
Question 10