An interesting geometry problem | Geometry | 70

In this video, we solve a nice geometry problem. At the end of the video, an exercise is included for viewers to try on their own. Check out this playlist which is a collection of geometry problems. https://www.youtube.com/playlist?list=PLo-BFz0Qjdz092Su4E09KKpTaux8fTIar Timecodes 0:00 - Description of the problem 0:47 - Using the collinearity of O, M and N to show that OM = 2√3 - r units 1:15 - Using the tangent radius theorem to show that ∠MPO = 90° 1:32 - Using Pythagoras's theorem to show that PO^2 = 12 - (4√3)r 2:11 - Using the tangent chord theorem and the angle at the center theorem to show that ∠QMP = 2α where ∠QPO = α 2:54 - Using the law of cosines in triangle MPQ to show that PQ^2 = 2r^2(1 - cos2α) 3:47 - Using the law of cosines in triangle POQ to show that PQ^2 = PO^2 + 1 - PO 4:13 - Using the law of sines in triangle POQ to show that sinα = √3/(2PQ) 4:53 - Forming an algebraic equation for r using previous results, then solving for r 7:46 - An exercise for viewers to try If you've enjoy this video, please like and subscribe for more content. Fundamental properties of circles Fundamental properties of triangles Relation between lines and circles Problem solving strategies Math olympiad preparation Math tricks #maths #education #mathematics #mathematicseducation #matholympiad #matholympiadtraining #geometry #problemsolving #mathstricks #geometrymath #howtosolvemathproblem #circle #triangle