Draw a circle with center at point Draw its chord AB and CD such that AB is not parallel to CD. Draw the perpendicular bisector of AB and CD. At what point do they intersect?

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Center of the circle

The perpendicular bisectors of any two chords will never meet

Both 1 and 2

None of the above

answer is A.

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Detailed Solution

Do stepwise construction of the question to reach to the point where they intersect.
Now we have a circle with centre O and it has two chords AB and CD such that both are non-parallel to each other.
So, let’s do it step by step.
Step 1: Draw a circle of any radius with center at O.
Step 2: In that circle draw two cords AB and CD, such that they are non-parallel.
Step 3: Now take radius (more than half of AB) and center as B draw two arcs, one on each side (left and right side) of the chord AB and name them as G and H.
Step 4: Similarly, draw two arcs taking center as A, cutting the previous arc G and H respectively.
Step 5: Draw a straight-line segment GH, such that it always passes through O.
Step 6: Now by taking C as center we have to repeat from step3 draw two arcs, one on each side (top and bottom) of chord CD, naming these as E and F.
Step 7: With center as D, and considering the same radius as taken in the before step, draw two arcs one on each side of the chord CD, cutting the previous arc E and F respectively.
Step8: Draw a straight-line segment EF, it always passes through O. Here we can clearly see that perpendicular bisectors of EF and GH intersect at center of the circle.
Hence, they are interested in the center of the circle.
So, option (1) is correct for this question.
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