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From Karnataka Open Educational Resources
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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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====== [[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:
+
+• Equal chords are equidistant from the centre.
+
+• Conversely, chords that are equidistant from the centre are equal.
====== [[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 ====
−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.
=====Activities=====
=====Activities=====
====== [[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.
−====== [[Properties of cyclic quadrilateral]] ======
+=====[[Properties of cyclic quadrilateral]]=====
+Relation between the angles of a cyclic quadrilateral are explored with this hand on activity.
==== 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.
====== [[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.
−====== [[Construction of cyclic quadrilateral]] ======
+====== [[Class10 circles tangents problems|Solved problems/ key questions (earlier was hints for problems).]] ======
−=====[[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
