SOLUTION: TWO PARALLEL CHORDS PQ AND MN ARE 3 cm APART ON THE SAME SIDE OF THE CIRCLE WHERE PQ=7 cm and MN = 14cm. CALCULATE THE RADIUS OF THE CIRCLE

Question 407869: TWO PARALLEL CHORDS PQ AND MN ARE 3 cm APART ON THE SAME SIDE OF THE CIRCLE WHERE PQ=7 cm and MN = 14cm. CALCULATE THE RADIUS OF THE CIRCLE

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Let and be the parallel chords with as of the circle
given:
and with distance between the parallel chords and .
Let and be the of and .
Then is a line which is the to both and
This is the theorem of the line joining the center of the circle and the mid point of the chord is perpendicular to the chord .
Or else, a line joining the center of the circle cuts chord perpendicularly, then it bisects the chord.

So, and
..........given
and
Let ,
now from the right angled triangle, , by Pythagoras theorem,
, where is the of the circle,
or
.........................(1)

Similarly from right triangle ,

or

...................(2).
From (1) and (2), left sides must be equal because right sides are equal:

.solve for

.
Therefore, from(1).

is the radius of the circle.

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