AB and AC are equal tangent to a circle which is 12 units in length. P is the centre of the circle. PD : DA = 3 : 10. Find the difference in area of circle and area of rhombus ABPC if an angle between the two radius is 106° and the area of sector is 23.17 sq.units.?

Question

AB and AC are equal tangent to a circle which is 12 units in length. P is the centre of the circle. PD : DA = 3 : 10. Find the difference in area of circle and area of rhombus ABPC if an angle between the two radius is 106° and the area of sector is 23.17 sq.units.?

23.56 sq.units
30.67 sq.units
32.45 sq.units
26.57 sq.units

LohaHridoy

5 views

2025-01-04 04:42

1 Answers

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AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 4 : 26.57 sq.units

Given:

Angle between two radius = 106°

Area of sector = 23.17

Then,

⇒ 23.17 = (106/360) × (22/7) × (r²)

Radius of circle = 5 units

Using tangent theorem,

In right angled triangle PBA,

Using Pythagoras theorem,

⇒ PA² = AB² + PB²

⇒ PA² = 144 + 25

⇒ PA = 13

Given:

⇒ PD : DA = 3 : 10

(∵ PA = PD + DA)

⇒ PD = 3

Then,

In right angled triangle PDB,

Using Pythagoras theorem,

⇒ PB² = PD² + BD²

⇒ BD = (25 – 9)^1/2

⇒ BD = 4

⇒ BC = 2BD = 8 Units

Area of circle = 22/7 × 25 = 78.57 sq.units

Area of rhombus = 1/2 × product of diagonals

Area of rhombus = 1/2 × 13 × 8

= 52 sq.units

Required difference =

= 78.57 – 52

= 26.57 sq.units