NCERT Class 9 Mathematics
CIRCLES 173 Though you have seen it for this particular case, try it out for other equal angles too. The chords will all turn ou ...
174 MATHEMATICS Theorem 10.4 : The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord. Is ...
CIRCLES 175 No. If the points lie on a line, then the third point will lie inside or outside the circle passing through two poin ...
176 MATHEMATICS Remark : If ABC is a triangle, then by Theorem 10.5, there is a unique circle passing through the three vertices ...
CIRCLES 177 A circle can have infinitely many chords. You may observe by drawing chords of a circle that longer chord is nearer ...
178 MATHEMATICS Fig. 10.23 them. This verifies the converse of the Theorem 10.6 which is stated as follows: Theorem 10.7 : Chord ...
CIRCLES 179 EXERCISE 10.4 Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is ...
180 MATHEMATICS Also the angle subtended by an arc at the centre is defined to be angle subtended by the corresponding chord at ...
CIRCLES 181 Also in ✂OAQ, OA = OQ (Radii of a circle) Therefore, ✁OAQ =✁OQA (Theorem 7.5) This gives ✁BOQ = 2 ✁OAQ (1) Similarly ...
182 MATHEMATICS You can see the truth of this result as follows: In Fig. 10.30, AB is a line segment, which subtends equal angle ...
CIRCLES 183 You find that ✁A + ✁C = 180° and ✁B + ✁D = 180°, neglecting the error in measurements. This verifies the following: ...
184 MATHEMATICS Example 5 : Two circles intersect at two points A and B. AD and AC are diameters to the two circles (see Fig.10. ...
CIRCLES 185 A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the m ...
186 MATHEMATICS Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect th ...
CIRCLES 187 Two congruent circles intersect each other at points A and B. Through A any line segment PAQ is drawn so that P, Q ...
CHAPTER 11 CONSTRUCTIONS 11.1 Introduction In earlier chapters, the diagrams, which were necessary to prove a theorem or solving ...
CONSTRUCTIONS 189 11.2 Basic Constructions In Class VI, you have learnt how to construct a circle, the perpendicular bisector of ...
190 MATHEMATICS Construction 11.2 : To construct the perpendicular bisector of a given line segment. Given a line segment AB, we ...
CONSTRUCTIONS 191 Fig. 11.3 Construction 11.3 : To construct an angle of 60^0 at the initial point of a given ray. Let us take a ...
192 MATHEMATICS included angle is given, (ii) three sides are given, (iii) two angles and the included side is given and, (iv) i ...
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