Q32 of 62 Page 10

Prove that the circle drawn with any side of a rhombus as diameter, passes through point of intersection of its diagonals.


We know that the diagonals of a rhombus bisect each other at right angles.
The circle drawn with one side AB as diameter will pass through the mid-point E of BD which is the point of intersection of the diagonals.

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30 The lengths of two parallel chords of a circle are 6cm and 8cm. If the smaller chord is at a distance of 4cm from the center, what is the distance of the other chord from the center? 31 Let the vertex of an angle ABC be located outside a circle and let the sides of the angle intersect equal chords AD and CE with the circle. Prove that ∠ABC is equal to half the difference of the angles subtended by the chords AC and DE at the center.
  33 ABCD is a parallelogram. The circle through A, B, and C intersect CD (produced if necessary) at E. Prove that AE = AD. 34 AC and BD are chords of a circle which bisect each other. Prove that AC and BD are diameters and ABCD is a rectangle.