SOLUTION: the shortest distance from the centre of a circle to a chord is 5 cm. find teh radius (2d.p.) of the circle if the chord is 3*2 times longer than the radius.

Algebra ->  Parallelograms -> SOLUTION: the shortest distance from the centre of a circle to a chord is 5 cm. find teh radius (2d.p.) of the circle if the chord is 3*2 times longer than the radius.      Log On


   

Question 108743: the shortest distance from the centre of a circle to a chord is 5 cm. find teh radius (2d.p.) of the circle if the chord is 3*2 times longer than the radius.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
I think the graph shows your problem.

You form a right triangle with sides 5 and (6+R)/2, and a hypotenuse of R.
Using the Pythagorean theorem,
%28%286%2BR%29%2F2%29%5E2%2B5%5E2=R%5E2
%28R%5E2%2B12R%2B36%29%2F4%2B25=R%5E2Expand the square.
%28R%5E2%2B12R%2B36%29%2B100=4R%5E2Multiply both sides by 4.
3R%5E2-12R-136=0 Group all terms on one side.
R+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
R+=+%28-%28-12%29+%2B-+sqrt%28+%28-12%29%5E2-4%2A3%2A%28-136%29+%29%29%2F%282%2A3%29+
R+=+%28%2812%29+%2B-+sqrt%28+%28144%2B1632%29%29%29%2F%286%29+
R+=+%28%2812%29+%2B-+sqrt%28+%281776%29%29%29%2F%286%29+
R+=+%28%2812%29+%2B-+42.14%29%2F%286%29+
R+=+%28%2812%29+%2B+42.14%29%2F%286%29+ Use only positive root, negative radius does not make sense in this application.
highlight%28R=9.02%29
Check your answer.
%28%286%2BR%29%2F2%29%5E2%2B5%5E2=R%5E2
%28%286%2B9.02%29%2F2%29%5E2%2B5%5E2=%289.02%29%5E2
%287.51%29%5E2%2B5%5E2=%289.02%29%5E2
56.4%2B25=81.4
81.4=81.4
True statement.
Good answer.
R=9.02 cm.