1 SUB GEOMETRY NAME OF TEACHER BHALERAO NANDKUMAR
1 SUB : -GEOMETRY NAME OF TEACHER : - BHALERAO NANDKUMAR KHANDERAO ASSTT. TEACHER SCHOOL : - NARSINHA VIDYALAYA RANJANI TAL-AMBEGAON, - DIST -PUNE.
4 Circle Std : IX Subject : Geometry Introduction : Respected sir, in previous standards we have already taught the techniques of drawing a circle of given radius , the distance between the centre of the circle and the chord , property of perpendicular drawn from the centre of the circle to its chord. , the property of distances between the centre and congruent chords of that circle.
Comparison between previous units and upgraded units of circle Units- arc of a circle, types of arc, central angle, angular measure of arc, angle subtended by arc in previous syllabus are deleted and included in the upgraded syllabus of X th std. But theorem , there is one and only one circle passing through the three non collinear points is newly added.
Subunits : 4. 1 Circle , related terms 4. 2 : points in a plane of circle 4. 3 : Circle passing through given points 4. 4 : Circles in a plane a) Concentric circles b) Congruent circles c) Intersecting circles 4. 5 Circle and line in a plane. 4. 6 : Angle subtended by chord ( Theorem and converse)
Defination of circle : A circle is a locus of points in a plane which are a constant distance from a fix point in that plane. Here fix point is called the centre of the circle.
and constant distance is called the radius of the circle. The M radius is shown. A B by the line r r segment from the centre to the circumference. The circle consist of all those points whose distance from the centre of the circle equals the radius. Diameter of the circle d = 2 r
m B Now we can recall previous knowledge of students which are obtained from above activities. A. O D l C 4. 1 Here Point O is the centre of the circle. Seg OC seg AD line m seg. AB ----- -------- line l
. T Points in plane of the circle A. M. L Circle is a simple closed. O figure which divides the plane into three disjoint parts. . P. Q. F Sr. no. Position 1 2 3 In the interior In the exterior On the circle D B . G Name of the points ………………. . ……………………
Point O is the centre and r is the radius of the circle If • OA = r then A is on the circle • OA > r then A is in the exterior of the circle • OA< r then A is in the interior of the circle . T B A . M. O. P . F . L. Q D . G
Circles in a plane: Given two circles in a Plane, there are following possibilities Concentric circles: Circles having same centre concentric circles and different radii are called Concentric circles. B O A
Congruent circles: Circles having equal radii are called congruent circles. Here PA and QB are circles with centers P and Q are congruent circles As PA = QB Q P A B
Intersecting circles: l) coplanar circles having two points in common are called intersecting circles. Here circles with centers P and Q are intersecting each other in two points namely A and B. A. P . Q B
ii) Coplanar circles intersecting in one point are called touching circles. In fig 4. 15 and 4. 16 circles with centres P and Q are touching in point A. . Q. P A . Q
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