This preview shows page 1. Sign up to view the full content.
PEM Level C
21 November 2009
Topics in Geometry  Basic Concepts and Theorems
Examples:
1. (PMO 198485) Let the rectangle
ABCD
be such that
AB
=
CD
= 4 units and
BC
=
AD
=
3 units. A perpendicular is dropped to the diagonal
BD
from each of the vertices
A
and
C
,
and let the feet of these perpendiculars be
P
and
Q
, respectively. Find
PQ
.
2. (PMO 198889, Modiﬁed) The base of a triangle is 15 cm. Two line segments are drawn
parallel to the base, terminating in the other two sides, and dividing the triangle into three
equal areas. Find the lengths of these two parallel segments.
3. (PMO 198485, Modiﬁed) A circle is inscribed in a square of side 8 cm. Inside one of the
corner spaces between the circle and the square, the largest possible circle is drawn. Find the
radius of this smaller circle.
4. A triangle has sides that measure 13, 14 and 15. A line perpendicular to the side of measure
14 divides the interior of the triangle into two regions (one is a triangle and the other is a
quadrilateral) of equal areas. What is the measure of the segment of the perpendicular that
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 11/15/2010 for the course MATH 100 taught by Professor B during the Spring '09 term at Ateneo de Manila University.
 Spring '09
 B
 Geometry

Click to edit the document details