In figure, AB and CD are equal chords of a circle whose centre is O. If OM ⊥ AB and ON ⊥ CD, prove that ∠OMN = ∠ONM.
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AB and CD are equal chords of a circle whose centre is O. When produced, these chords meet at E. Prove that EB = ED and AE = CE.
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43.Bisector AD of ∠BAC of ∆ABC passes through the centre O of the circumcircle of ∆ABC. Prove that AB = AC.
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44.In figure, AB and AC are two equal chords of a circle whose centre is O. If OD ⊥ AB and OE ⊥ AC, prove that ADE is an isosceles triangle.
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45.If two intersecting chords of a circle make equal angles with the diameter passing through their point of intersection, prove that the chords are equal.
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46.In figure, AB and CD are two chords of a circle with centre O. The two chords intersect each other at the point P. If PO bisects ∠APD, prove that AB = CD.
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47.In the given figure, two chords AB and CD of a circle, with centre O, are such that OP and OQ, the perpendiculars from the centre to the chords, are equal. Show that AB = CD.
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48.Prove that the line segment joining the mid-points of two equal chords of a circle makes equal angles on its same side with the chords.
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49.Prove that the chords equidistant from the centre of a circle are equal in length.
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50.PQ and RQ are chords of a circle equidistant from the centre. Prove that the diameter passing through Q is the bisector of ∠PQR.