Try this beautiful problem from the Pre-RMO II, 2019, Question 28, based on Length of side of triangle.

Length of side of triangle – Problem 28

In a triangle ABC, it is known that \(\angle\)A=100\(^\circ\) and AB=AC. The internal angle bisector BD has length 20 units. Find the length of BC to the nearest integer, given that sin 10\(^\circ\)=0.174.

  • is 107
  • is 27
  • is 840
  • cannot be determined from the given information

Key Concepts




Check the Answer

But try the problem first…

Answer: is 27.

Suggested Reading

PRMO II, 2019, Question 28

Higher Algebra by Hall and Knight

Try with Hints

First hint

given, BD=20 units



In \(\Delta\)ABD


or, \(\frac{BD}{sin100^\circ}=\frac{AD}{sin20^\circ}\)

or, 20=\(\frac{AD}{2sin10^\circ}\) or, AD=40sin10\(^\circ\)=6.96

finding the length of the side of triangle

Second Hint

In \(\Delta\)BDC


or, CD=\(\frac{20}{2cos20^\circ}\)=\(\frac{20}{2 \times 0.9394}\)=10.65

Final Step

So, AD+CD=AC=AB=17.6

since BD is angle bisector


or, BC=\(\frac{AB \times CD}{AD}\)=\(\frac{17.6 \times 10.65}{6.96}\)


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