What is the NO-SHORTCUT approach for learning great Mathematics?

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Try this beautiful problem from Geometry based on Trapezium.

Let ABCD be a trapezium in which AB||CD and AD is perpendicular on AB .suppose has an incircle which touches AB at Q and CD at P.Given that PC=36 and QB=49. Find PQ?

- $64$
- $81$
- $84$

Geometry

Trapezoid

Circle

But try the problem first...

Answer:$84$

Source

Suggested Reading

PRMO-2018, Problem 5

Pre College Mathematics

First hint

Let the radius of the inner circle be r

Therefore AQ=PD=r and AD=2r

Can you now finish the problem ..........

Second Hint

Draw a perpendicular from C on AB at the point F

Can you finish the problem........

Final Step

Let the inner circle touches BC at E

Then CE=36 (as BE & BQ are tangents)

BE=49 (as CE & PC are tangents)

Let the radius of the inner circle be r

Therefore AQ=PD=r and AD=2r

Let draw a perpendicular from C on AB at the point F

So BF=(AB-AF)=(49-36)=13

BC=85

Now in the triangle CBF we have

\(CF^2=85^2-13^2\)

\(\Rightarrow CF=84\)

Therefore CF=PQ=84

- https://www.youtube.com/watch?v=dLHUPDQzc2Q
- https://www.cheenta.com/largest-and-smallest-numbers-amc-8-2006-problem-22/

What to do to shape your Career in Mathematics after 12th?

From the video below, let's learn from Dr. Ashani Dasgupta (a Ph.D. in Mathematics from the University of Milwaukee-Wisconsin and Founder-Faculty of Cheenta) how you can shape your career in Mathematics and pursue it after 12th in India and Abroad. These are some of the key questions that we are discussing here:

- What are some of the best colleges for Mathematics that you can aim to apply for after high school?
- How can you strategically opt for less known colleges and prepare yourself for the best universities in India or Abroad for your Masters or Ph.D. Programs?
- What are the best universities for MS, MMath, and Ph.D. Programs in India?
- What topics in Mathematics are really needed to crack some great Masters or Ph.D. level entrances?
- How can you pursue a Ph.D. in Mathematics outside India?
- What are the 5 ways Cheenta can help you to pursue Higher Mathematics in India and abroad?

Cheenta has taken an initiative of helping College and High School Passout Students with its "Open Seminars" and "Open for all Math Camps". These events are extremely useful for students who are really passionate for Mathematic and want to pursue their career in it.

Cheenta is a knowledge partner of Aditya Birla Education Academy

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.

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