CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

Circle Exercise Ex. 17(A)


Solution 1


Let AB be the chord and O be the centre of the circle.

Let OC be the perpendicular drawn from O to AB.

198581 image001 CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

We know, that the perpendicular to a chord, from the centre of a circle, bisects the chord.

AC = CB = 3 cm

198581 image003 CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

Solution 2

198583 image004 CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER


Let AB be the chord and O be the centre of the circle.

Let OC be the perpendicular drawn from O to AB.

198583 image005 CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

We know, that the perpendicular to a chord, from the centre of a circle, bisects the chord.

198583 image006 1 CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

Hence, radius of the circle is 5 cm.

Solution 3

198585 image007 CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER


Let AB be the chord and O be the centre of the circle.

Let OC be the perpendicular drawn from O to AB.

We know, that the perpendicular to a chord, from the centre of a circle, bisects the chord.

AC = CB

198585 image008 CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

Solution 4

198587 image009 2 CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER


Let AB be the chord of length 24 cm and O be the centre of the circle.

Let OC be the perpendicular drawn from O to AB.

We know, that the perpendicular to a chord, from the centre of a circle, bisects the chord.

AC = CB = 12 cm

198583 image006 1 1 CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER


Solution 5

CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

For the inner circle, BC is a chord and .

We know that the perpendicular to a chord, from the centre of a circle, bisects the chord.

BP = PC

For the outer circle, AD is the chord and.

We know that the perpendicular to a chord, from the centre of a circle, bisects the chord.

AP = PD

By Pythagoras Theorem,

OA2 = OP2 + AP2

=> AP2 = (34)2 – (16)2 = 900

=> AP = 30 cm

AB = AP – BP = 30 – 12 = 18 cm

Solution 6

CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER
CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER


Let O be the centre of the circle and AB and CD be the two parallel chords of length 30 cm and 16 cm respectively.

Drop OE and OF perpendicular on AB and CD from the centre O.

Solution 7

CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER


Since the distance between the chords is greater than the radius of the circle (15 cm), so the chords will be on the opposite sides of the centre.

Let O be the centre of the circle and AB and CD be the two parallel chords such that AB = 24 cm.

Let length of CD be 2x cm.

Drop OE and OF perpendicular on AB and CD from the centre O.

Solution 8

CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

Solution 9

CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

Let the radius of the circle be r cm.

CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

Solution 10

CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

Circle Exercise Ex. 17(B)


Solution 1

Circle Exercise Ex. 17(A)

CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

Solution 2

Circle Exercise Ex. 17(A)

Circle Exercise Ex. 17(A)

Solution 3

CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

Circle Exercise Ex. 17(A)

Solution 4


Drop OM and O’N perpendicular on AB and OM’ and O’N’ perpendicular on CD.

Circle Exercise Ex. 17(A)

Circle Exercise Ex. 17(A)

Solution 5


Drop OM and ON perpendicular on AB and CD.

Join OP, OB and OD.

Circle Exercise Ex. 17(A)

Circle Exercise Ex. 17(A)

Solution 6

CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

Solution 7

Circle Exercise Ex. 17(A)

Circle Exercise Ex. 17(A)

Solution 8

Circle Exercise Ex. 17(A)

Solution 9

Circle Exercise Ex. 17(A)

Solution 10

Circle Exercise Ex. 17(A)

Circle Exercise Ex. 17(A)

Circle Exercise Ex. 17(C)


Solution 1

Circle Exercise Ex. 17(A)
Circle Exercise Ex. 17(A)

Solution 2

Circle Exercise Ex. 17(c) 2 supremetutorials

Circle Exercise Ex. 17(c) 2 supremetutorials

Solution 3

Circle Exercise Ex. 17(c) 2 supremetutorials

Solution 4

Circle Exercise Ex. 17(c) 4 supremetutorials

Circle Exercise Ex. 17(c) 4 supremetutorials(2)

Solution 5

Circle Exercise Ex. 17(c) 4 supremetutorials(2)

Solution 6

CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

Solution 7

CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

Solution 8

CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

Circle Exercise Ex. 17(D)


Solution 1

CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER
CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

Solution 2

CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

Solution 3

CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

So, the circle can have 0, 1 or 2 points in common.

The maximum number of common points is 2.

Solution 4

CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

Solution 5

CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

Solution 6

CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER
CLASS 9 ICSE/CBSE BOARDS CIRCLE FULL CHAPTER

Solution 7

Solution 8

Solution 9

Solution 10


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