The point A lies on the circle C, with centre O and radius r. The circle C₂ wit centre A and radius r√3 intersects C₁ at the points B and C, as shown in the diagram. A r√√3 r r√3 B C C₁ (i) Using the cosine rule (or otherwise) find ZBAO. (ii) Find the area of the sector BAC of C₂. (iii) Find the area of the sector BOC of C₁ . (iv) Hence (or otherwise) find the area of the shaded region.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 74E
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Part iii & iv

The point A lies on the circle ₁ with centre O and radius r. The circle ₂ with
centre A and radius r√3 intersects C₁ at the points B and C, as shown in the
diagram.
A
r√√3
r
r√√3
B
C
(i) Using the cosine rule (or otherwise) find ZBAO.
(ii)
Find the area of the sector BAC of C₂.
(iii) Find the area of the sector BOC of C₁.
(iv)
C₁
Hence (or otherwise) find the area of the shaded region.
Transcribed Image Text:The point A lies on the circle ₁ with centre O and radius r. The circle ₂ with centre A and radius r√3 intersects C₁ at the points B and C, as shown in the diagram. A r√√3 r r√√3 B C (i) Using the cosine rule (or otherwise) find ZBAO. (ii) Find the area of the sector BAC of C₂. (iii) Find the area of the sector BOC of C₁. (iv) C₁ Hence (or otherwise) find the area of the shaded region.
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