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October 13, 2020

How to Pursue Mathematics after High School?

For Students who are passionate for Mathematics and want to pursue it for higher studies in India and abroad.

Try this beautiful Trigonometry Problem based on Measure of Angle from PRMO -2018.

Measure of Angle - PRMO 2018- Problem 29


Let $D$ be an interior point of the side $B C$ of a triangle ABC. Let $l_{1}$ and $l_{2}$ be the incentres of triangles $A B D$ and $A C D$ respectively. Let $A l_{1}$ and $A l_{2}$ meet $B C$ in $E$ and $F$ respectively. If $\angle B l_{1} E=60^{\circ},$ what is the measure of $\angle C l_{2} F$ in degrees?

,

  • \(25\)
  • \(20\)
  • \(35\)
  • \(30\)
  • \(45\)

Key Concepts


Trigonometry

Triangle

Angle

Suggested Book | Source | Answer


Suggested Reading

Pre College Mathematics

Source of the problem

Prmo-2018, Problem-29

Check the answer here, but try the problem first

\(30\)

Try with Hints


First Hint

Measure of Angle

According to the questations at first we draw the picture . We have to find out the value of

$\angle C l_{2} F$. Now at first find out \(\angle AED\) and \(\angle AFD\) which are the exterioe angles of \(\triangle BEL_1\) and \(\triangle CL_2F\). Now sum of the angles is $180^{\circ}$

Now can you finish the problem?

Second Hint

$\angle E A D+\angle F A D=\angle E A F=\frac{A}{2}$
$\angle A E D=60^{\circ}+\frac{B}{2}$
$\angle A F D=\theta+\frac{C}{2}$
Therefore $\quad \ln \Delta A E F: \frac{A}{2}+60^{\circ}+\frac{B}{2}+\theta+\frac{C}{2}=180^{\circ}$
$90^{\circ}+60^{\circ}+\theta=180^{\circ}$ (as sum of the angles of a Triangle is $180^{\circ}$
Therefore $\quad \theta=30^{\circ}$

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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?

Want to Explore Advanced Mathematics at Cheenta?

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.

To Explore and Experience Advanced Mathematics at Cheenta
Register here

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