Name: _______________________
Common Core Geometry - Honors
Date: _________________
Concurrency – Day 2
1.) The centroid of a triangle divides the medians into a ratio of
(1) 3:1
(2) 4:1
(3) 2:1
(4) 5:1
2.) The point where the altitudes are concurrent is called the _____________.
3.) The point where the perpendicular bisectors are concurrent is called the
_______________.
4.) The point where the angle bisectors are concurrent is called the _____________.
5.) You are looking at a triangle where the orthocenter, the centroid and the circumcenter
are all the same point. What type of triangle are you looking at?
(1) Scalene
(2) Isosceles
(3) Equilateral
(4) Right
6.) The centroid of a triangle is located 12 units from one of the vertices of a triangle.
Find the length of the median of the triangle drawn from that same vertex.
7.) Given that point O is the incenter of isosceles triangle ABC and that the
vertex angle C measures 100°.
a.) m<BOE = ________
b.) m<ADB = ________
c.) m<AEC = _________
8.) If point H is the circumcenter of right triangle ABC and point O is the incenter
of right triangle ABC, what is the value of ‘x’, the area of the incircle, and the area
of the circumscribed circle given that AC = 8, AB = 10, EB = 4 and CE = x?
a.) Find the value of x.
b.) Find the area of the incircle, in terms of π.
c.) Find the area of circumscribed circle, in terms of π.
9.) In the diagram of ΔABC below, Jose found centroid, P, by constructing the
three medians. He measured
and found it to be 6 inches.
If PF = x :
a.) Write an equation that represents the length of CF.
b.) Solve the equation in part a, to find PF.