A Geometry Problem Using Perpendiculars and Midpoints

Описание: Hello students
In this video, we solve a non-routine geometry problem involving a right-angled triangle, midpoints, perpendiculars, and trigonometric reasoning.

Given in the problem:
A triangle ABC with a right angle at B
Angle A=45∘
Side BC=8
Points D and E are midpoints of sides
Perpendicular bisectors and perpendiculars intersect at points F and G
You are asked to find the value of BF × CG
At first, the construction looks complicated, but the problem becomes manageable when broken into smaller right-angled triangles.

Key ideas used in this solution:
Properties of midpoints and perpendicular bisectors
Using trigonometric ratios in right-angled triangles
Expressing lengths in terms of sine and cosine
Applying the Sine Rule at the final step
Combining geometry with trigonometry in a clean way
This problem is a great example of how geometry and trigonometry work together in advanced mathematics exams.

Suitable for:
Math Olympiad aspirants
Pre-RMO
NMTC (Aryabhata Stage-2)
IMO/NSO foundation students
Class 9 & 10 students preparing for advanced problems

Follow the construction carefully
Track each right-angled triangle step by step
Focus on logic, not memorisation

If you found this video useful:
Like the video
Subscribe for more non-routine geometry problems
Comment if you want similar questions explained

#MathsOlympiad #GeometryProblem #NonRoutineProblems #PreRMO #NMTC #AryabhataStage2 #Trigonometry #AdvancedGeometry #Class9Maths #ProblemSolving