Geometry Question?

Question

Construct a line segment AFOD such that FO = OD.  Now construct a semi-circle such that FOD is a diameter and O is the origin of the circle.   Construct a line segment ABC, non-colinear with AFD, such that C lies on the semi-circle and the line sement intersects the semicircle at B.  (When you draw this out, it is easiest to see if you place C on the "D" side of the quarter circle and B on the "F" side of the quarter circle).  If AB = OC, what is the angle measurement of BAO?

1)  The angle measure of COD is 60°
2)  The angle measure of BCO is 40°

A)  This may be solved with eqn (1) alone.
B)  This may be solved with eqn (2) alone.
C)  This may be solved using eqn(1) and eqn(2) but not with each alone.
D)  This may be solved with either eqn(1) or eqn(2) alone
E)  There is not enough info from either eqn to solve the problem.

I said the answer was B but the correct answer is D.  Can anyone explain?

Grampedo · Accepted Answer

COD=60
This angle is an exterior angle to triangle ACO
As such, it is equal to the sum of the interior and
opposite angles.
One of the interior and opposite angles, (angle ACO)
is 40. Therefore the other interior and opposite angle
(BAO) must be 60-40=20
This solution uses Eq'n. 2 alone. It seems clear to me
that you got the Eq'n.1 solution, so I won't repeat
what you've already solved.

Tom K · Answer

D is correct.  If you draw it out and mark the lengths that are equal, you will see that triangle ABO and triangle BCO are each isosceles.  This means that angle BAO = angle AOB and their sum is equal angle OBC, which is equal to angle BCO.  Translation: angle BAO = 1/2 angle BCO.
Angle BAO + angle BCO also = angle COD because that total is the supplement of angle AOC.

In summary:
angle BAO = 1/3 angle COD or angle COD = 3*angle BAO
angle OCB = 2/3 angle COD or angle COD = 1.5*angle OCB
Knowing any of the angles tells you what the others are.

Trending News

Geometry Question?

2 Answers