How Cheenta works to ensure student success?
Explore the Back-Story

Diameter of a circle | PRMO 2019 | Question 25

Join Trial or Access Free Resources

Try this beautiful problem from the Pre-RMO, 2019 based on Diameter of a circle.

Diameter of a circle - PRMO 2019

A village has a circular wall around it, and the wall has four gates pointing north, southeast and west. A tree stands outside the village, 16 m north of the north gate, and it can be just seen appearing on the horizon from a point 48 m east of the south gate. Find the diameter in meters of the wall that surrounds the village.

  • is 107
  • is 48
  • is 840
  • cannot be determined from the given information

Key Concepts

Pythagoras Theorem



Check the Answer

Answer: is 48.

PRMO, 2019, Question 25

Geometry Vol I to IV by Hall and Stevens

Try with Hints

Let radius =r



or, \(AD^{2}+DC^{2}=CA^{2}\)

Diameter of a circle - figure

or, \(48^{2}+(2r+16)^{2}\)


or, \(r^{2}+8r=24\sqrt{256+32r}\)

or, \(r(r+8)=24(4\sqrt{2})(\sqrt{r+8})\)

or, r=24

or, 2r=diameter=48.

Subscribe to Cheenta at Youtube

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy

Cheenta Academy

Aditya Birla Education Academy

Aditya Birla Education Academy

Cheenta. Passion for Mathematics

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