PR - Geo Question - Need help

IMO D
From I
first get AB--then r can be found
from II
again area, r can be found

In (B) I don't understand how can you find r by just knowing the area of the triangle. All we know is:

1. Triangle is isosceles with two sides = r
2. Area of the triangle

Here is how you get r by knowing AD:

Draw a line from A to O. Now we have triangle AOD.

We know AO is r, OD is (r-2), and AD is 6.

You can see we could solve for r using the Pythagorean theorum. Thus, knowing AD is sufficient to solve for r.

Of course, now we could solve for circumference because it is 2pir.

Hope that helped,

Tatiana

Tatiana, that solves for A, how about the option B? In your opinion, is B sufficient to solve for r? If yes, then how?

VP_Tatiana wrote:Here is how you get r by knowing AD:

Draw a line from A to O. Now we have triangle AOD.

We know AO is r, OD is (r-2), and AD is 6.

You can see we could solve for r using the Pythagorean theorum. Thus, knowing AD is sufficient to solve for r.

Of course, now we could solve for circumference because it is 2pir.

Hope that helped,

Tatiana

From 2:

Area of triangle 1/2 *base*alt=50

here base=alt=radius of traingle


so 1/2r^2=50
r=10

You are assuming the triangle is a right angle triangle. The question doesn't say that its a right angle triangle. This is of course my read on the question and I may be wrong hence need to understand why everyone is interpreting the triangle to be right angled.

amitansu wrote:From 2:

Area of triangle 1/2 *base*alt=50

here base=alt=radius of traingle


so 1/2r^2=50
r=10

amitansu wrote:From 2:

Area of triangle 1/2 *base*alt=50

here base=alt=radius of traingle


so 1/2r^2=50
r=10

I am confused, how exactly did you reach the conclusion that base = alt=radius. This would be true only if OBC is a isosceles right angle triangle. The question gives no indication of this. I believe the answer should be A, the solution for which is already provided.

BTW the OA by PR for this is D. Explanation assumes the tirangle to the right angled. Anyone know how to give feedback to PR about this error.

Cant we use the formula for Isosceles Triangle ??

Yes, there could be a misprint in book.Right angle has to be assumed here.But not necessarily isoseceles triangle !!

Because, for triangle OBC it shows the two sides are nothing but radii.

So the formula can be reduced to 1/2 alt*base=50
=> 1/2*r*r=50

Sandeep, the formula you have posted can not be used because one variable in the formula is the base of the triangle and the other is one of the equal sides.

Amit, I also think this is an error on part of PR. This problem is from one of their tests and not from the book.