The document describes a problem in mensuration involving finding the area of a circle given information about two perpendicular chords inside the circle. It is given that AP = 6 cm, PB = 4 units, and DP = 3 units. Using properties of perpendicular chords and the fact that a line drawn from the center perpendicular to a chord bisects the chord, the radius of the circle is found to be 5 cm. The area of a circle formula is then used, and it is determined that the area is 125π/4 square cm, which is answer choice a.

1. Mensuration

2. Mensuration
Two mutually perpendicular chords AB and CD meet at a point P
inside the circle such that AP = 6 cms, PB = 4 units and DP = 3 units.
What is the area of the circle?
(a)
125π
4
sq cms (b)
100π
7
sq cms
(c)
125π
8
sq cms (d)
52π
3
sq cms

3. Mensuration
Two mutually perpendicular chords AB and CD meet at a point P
inside the circle such that AP = 6 cms, PB = 4 units and DP = 3 units.
What is the area of the circle?
?

4. Mensuration
Two mutually perpendicular chords AB and CD meet at a point P
inside the circle such that AP = 6 cms, PB = 4 units and DP = 3 units.
What is the area of the circle?

5. Mensuration
As AB and CD are two chords that intersect at O, AP × PB = CP × PD
6 × 4 = CP × 3
CP = 8
From center O draw OM r AB and ON r CD
From the center a line  r to a chord bisects the chord.
Two mutually perpendicular chords AB and CD meet at a point P
inside the circle such that AP = 6 cms, PB = 4 units and DP = 3 units.
What is the area of the circle?

6. Mensuration
So, we have AM = MB = 5 cm
MP = 1 cm, ON = 1 cm, CD = 11 cm, CN = 5.5 cm
ON2 + CN2 = OC2
12 + 5.52 + r2
1 + 30.25 = r2
Two mutually perpendicular chords AB and CD meet at a point P
inside the circle such that AP = 6 cms, PB = 4 units and DP = 3 units.
What is the area of the circle?

7. Mensuration
Area = pr2
p × 31.25
31.25p =
125π
4
Answer choice (a)
Two mutually perpendicular chords AB and CD meet at a point P
inside the circle such that AP = 6 cms, PB = 4 units and DP = 3 units.
What is the area of the circle?

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