The document discusses calculating the area of a quadrilateral shape formed inside a circle. It defines the length of a chord in a circle and shows a diagram with a diameter AB and parallel chord PQ. It then finds the length of a perpendicular from the center C to the chord PQ, allowing the area of the quadrilateral PABQ to be determined using properties of chords, perpendiculars, radii, and the Pythagorean theorem.

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