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From Karnataka Open Educational Resources
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, 06:39, 21 May 2019
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| ====== [[Congruent chords are equidistant from the centre of a circle|Congruent chords are equidistant from the center of a circle]] ====== | | ====== [[Congruent chords are equidistant from the centre of a circle|Congruent chords are equidistant from the center of a circle]] ====== |
| + | In the same circle or in circles of equal radius: |
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| + | • Equal chords are equidistant from the centre. |
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| + | • Conversely, chords that are equidistant from the centre are equal. |
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| ====== [[Angles in a circle subtended by a chord]] ====== | | ====== [[Angles in a circle subtended by a chord]] ====== |
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| ==== Concept #5: Cyclic Quadrilateral ==== | | ==== Concept #5: Cyclic Quadrilateral ==== |
− | A quadrilateral ABCD is called cyclic if all four vertices of it lie on a circle.In a cyclic quadrilateral the sum of opposite interior angles is 180 degrees.If the sum of a pair of opposite angles of a quadrilateral is 180, the quadrilateral is cyclic.In a cyclic quadrilateral the exterior angle is equal to interior opposite angle.
| + | In Euclidean geometry, a '''cyclic quadrilateral''' or inscribed '''quadrilateral''' is a '''quadrilateral''' whose vertices all lie on a single circle. This circle is called the circumcircle or circumscribed circle, and the vertices are said to be concyclic. |
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| =====Activities===== | | =====Activities===== |
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| ====== [[Cyclic quadrilateral]] ====== | | ====== [[Cyclic quadrilateral]] ====== |
| + | A quadrilateral ABCD is called cyclic if all four vertices of it lie on a circle.In a cyclic quadrilateral the sum of opposite interior angles is 180 degrees.If the sum of a pair of opposite angles of a quadrilateral is 180, the quadrilateral is cyclic.In a cyclic quadrilateral the exterior angle is equal to interior opposite angle. |
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− | ====== [[Properties of cyclic quadrilateral]] ====== | + | =====[[Properties of cyclic quadrilateral]]===== |
| + | Relation between the angles of a cyclic quadrilateral are explored with this hand on activity. |
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| ==== Concept #6 Constructions in circles ==== | | ==== Concept #6 Constructions in circles ==== |
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| ====== [[Construction of direct common tangent]] ====== | | ====== [[Construction of direct common tangent]] ====== |
| + | The direct common tangents to two circles meet on the line of centres and divide it externally in the ratio of the radii. |
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| ====== [[Construction of transverse common tangent]] ====== | | ====== [[Construction of transverse common tangent]] ====== |
| + | The transverse common tangents also meet on the line of centres and divide it internally in the ratio of the radii. |
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− | ====== [[Construction of cyclic quadrilateral]] ====== | + | ====== [[Class10 circles tangents problems|Solved problems/ key questions (earlier was hints for problems).]] ====== |
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− | =====[[Class10 circles tangents problems|Solved problems/ key questions (earlier was hints for problems).]]===== | |
| ===Projects (can include math lab/ science lab/ language lab) === | | ===Projects (can include math lab/ science lab/ language lab) === |
| #Collect different types of circular objects | | #Collect different types of circular objects |