powerponit presentation

1. CIRCLES
Chords of circle

2. Length of the chord
A B
Length of the chord AB= 2√ r 2 - d2

3. Quadrilaterals
A B P Q
C D R S
U W
X Y

4. In the figure below AB is the diameter of
the circle and PQ is a chord parallel to it .
Compute the area of the quadrilateral
P 8 cm
Q
C
*
A B
1
1
16 cm

5. C is the centre of the circle. AB is the
diametre. Draw a perpendicular from C to
PQ and mark it as R.
*
C
P
R
A
Q
B

6. • The perpendicular from the centre of
the circle to the chord passes
through the midpoint of the chord
• Given AB = 16 cm.
AC = 8cm & BC = 8cm
• Since R is the midpoint of PQ,
PR = 4cm & RQ = 4cm.
• Join CQ

7. CQ = 8cm( Radius)
4cm 4cm
P Q
By Pythagoras theorem,
Hypotenuse = Base + Altitude
CR = √CQ - QR
= √ 8 - 4
= √ 64 - 16
= √ 48
= 4√3cm
R
C
A
B
8cm 8cm
2 2 2
2
2
2
2

8. Area of trapezium ABQP = ½ CR[PQ + AB]
= ½ 4 √3[8 + 16]
= 2 √3 × 24
= 48 √3 sq.cm