Tricky Circle!!

Geometry Level 2

A and B are two points on a circle with a centre O and C lies outside the circle , on ray AB. If AB = 24 , BC =28 , OA = 15 then find OC.


The answer is 41.

Aman Agrawal by Aman Agrawal , 23, India

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3 solutions

Sharad Gaikwad
Apr 3, 2014

If you draw a perpendicular from O on AB, let foot of perpendicular be D, then by Pythagoras theorem AD= 9 cm and DC = 12+28= 40 cm and again by Pythagoras theorem CD= 41 cm

2 Helpful 0 Interesting 0 Brilliant 0 Confused

try to put point C where no right triangle would be formed, it's just a point outside a circle right? You'll get lost :) just my comment, no offense

Marchan Sy - 7 years, 1 month ago

How can you figure out AD if we don't know OD? Pls tell

Kriti Goel - 6 years, 10 months ago
Zakaria Salameh
May 24, 2014

draw OB =15cm and use cosines rule for ABO to find angle ABO=36.87 then use cosines rule again for triangle OCB where OB =15 BC=28 & angle OBC=143.13 to get the value of OC =41cm

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Marchan Sy
May 6, 2014

Though I was able to answer this problem, still I believe that this problem is a real problem because the information given is not enough. I think he should point out that points A, B and C are collinear because if that was given, then you would actually get 41 as an answer or at least provide a clear figure about the problem.

I said this because the distance between points O and C depends on where is it place with respect to the other points. All that's stated in the problem is that C is a point outside the circle. If you try not make C collinear to points A and B, You'll definitely get a different answer.

This problem is not really tricky but its just that it could give you infinite solutions, depending on where you put point C with respect to the 3 given points.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

please explain there is doubt according to pythagorous theorem .

amar nath - 7 years ago

I'ts stated that C lies on AB ,if you read carefully

Constantin Merlusca - 6 years, 11 months ago

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