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Tuesday , August 22 2017
Home / Geometry (page 5)

Geometry

Prove that if two chords of a circle bisect each other, their point of intersection is the centre of the circle.

General enunciation: If two chords of a circle bisect each other, we have to show that their point of intersection is the centre of the circle. Particular enunciation: Suppose two chords AC and BD of the circle ABCD bisect each other at the point O i.e., OA = OC and ...

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Prove that the line segment joining the middle point of the hypotenuse of a right angle triangle and the opposite vertex is half the hypotenuse.

General enunciation: We have to prove that the line segment joining the middle point of the hypotenuse of a right angle triangle and the opposite vertex is half the hypotenuse. Particular enunciation: Suppose in right angle triangle ∆ABC, ∠B=900 and AC is hypotenuse. BO is the line joining the middle ...

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In the triangle ABC, AB>AC and the bisectors of the ∠B and ∠C intersect at the point P. Prove that PB>PC.

General enunciation: In the triangle ABC, AB>AC and the bisectors of the ∠B and ∠C intersect at the point P. Prove that PB>PC. Particular enunciation: In the triangle ABC, AB>AC and the bisectors of the ∠B and ∠C intersect at the point P. It is required prove that PB>PC. Proof: ...

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In the ∆ABC, the internal bisector of the ∠B and ∠C intersects at the point D. Prove that ∠BDC = 90°-½∠A.

Solution: General enunciation: In the ∆ABC, the internal bisector of the ∠B and ∠C intersects at the point D. We have to prove that ∠BDC = 90°-½∠A. Particular enunciation: In the ∆ABC, the internal bisector of the ∠B and ∠C is BD and CD intersects at the point D. ° ...

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In the ∆ABC, the internal bisector of the ∠B and ∠C intersects at the point D. Prove that ∠BDC = 90° +½∠A .

Solution: General enunciation: In the ∆ABC, the internal bisector of the ∠B and ∠C intersects at the point D. We have to prove that ∠BDC = 90° +½∠A. Particular enunciation: In the ∆ABC, the internal bisector of the ∠B and ∠C is BD and CD intersects at the point D. ...

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Prove that, if the diagonals of a quadrilateral bisect each other, it is a parallelogram.

Solution: General enunciation: To prove that if the diagonals of a quadrilateral bisect each other, it is a parallelogram. Particular enunciation: Let the diagonals AC and BD of the quadrilateral ABCD bisect each other at O. We have to prove that ABCD is a parallelogram. Proof: The diagonals AC and ...

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