figure shows sector of circle ,centre O , containing an angle theta P.T
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2
Step-by-step explanation:
my process Uses tHe RHS to derive LHS.
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Answer:
prooved above
Step-by-step explanation:
Perimeter of the shaded region
= arc AC + AB + BC
Arc AC = Φ * 2πr / 360
= Φ π r /180
Tan Φ = AB /OA
= AB /r
AB = r tan Φ
Similarly,
BC = OB -OC
= rsec Φ -r
= r(secΦ-1)
☞Perimeter = arc AC+AB+AC
= Φπr/180+ rtanΦ + rsecΦ-r
= r(tanΦ +sec Φ +π Φ/180-1)
☆Hence, your first part is proved !
☞ Area :
= Area of right triangle OAB - Area of
sector
= 1/2 *OA *AB - Φ *πr^2 /360
= r^2tanΦ/2 - πr^2 Φ /360
= r^2 /2 ( tan Φ -π Φ/180
hope it helps you
don't mark as brainest
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