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Circles

If non-parallel sides of a trapezium are equal, prove that it is cyclic

06/11/2024

Mathematics

9th

Circles

If two equal chords of a circle intersect, prove that the parts of one chord are separately equal to the parts of the other chord.

06/11/2024

Mathematics

9th

Circles

Prove that among all the chords of a circle passing through a given point inside the circle that one is smallest which is perpendicular to the diameter passing through the point.

06/11/2024

Mathematics

9th

Circles

Prove that two circles cannot intersect at more than two points

06/11/2024

Mathematics

9th

Circles

Two circles with centres O and O′ intersect at two points A and B. A line PQ is drawn parallel to OO′ through A(or B) intersecting the circles at P and Q. Prove that PQ = 2 OO′.

06/11/2024

Mathematics

9th

Circles

A quadrilateral ABCD is inscribed in a circle such that AB is a diameter and ∠ADC = 130º. Find ∠BAC.

06/11/2024

Mathematics

9th

Circles

A chord of a circle is equal to its radius. Find the angle subtended by this chord at a point in major segment

06/11/2024

Mathematics

9th

Circles

The circumcentre of the triangle ABC is O. Prove that ∠OBC + ∠BAC = 90º.

06/11/2024

Mathematics

9th

Circles

If a pair of opposite sides of a cyclic quadrilateral are equal, prove that its diagonals are also equal.

06/11/2024

Mathematics

9th

Circles

If a line is drawn parallel to the base of an isosceles triangle to intersect its equal sides, prove that the quadrilateral so formed is cyclic.

06/11/2024

Mathematics

9th