25

Part of 2019 India PRMO

Problems(2)

Simple Geometry word problem involving circles and tangents

Source:

A village has a circular wall around it, and the wall has four gates pointing north, south, east and west. A tree stands outside the village,

16 \, \mathrm{m}

north of the north gate, and it can be just seen appearing on the horizon from a point

48 \, \mathrm{m}

east of the south gate. What is the diamter in meters, of the wall that surrounds the village?

geometryTangents

Source: PRMO Leg 2 P25

ABC

be an isosceles triangle with

AB=BC

. A trisector of

\angle B

AC

D

AB,AC

BD

are integers and

AB-BD

=

3

AC