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How to Edit Text for Your O1ce with Adobe DC on Windows

Adobe DC on Windows is a useful tool to edit your file on a PC. This is especially useful when you prefer to do work about file edit in the offline mode. So, let'get started.

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How to Edit Your O1ce With Adobe Dc on Mac

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How to Edit your O1ce from G Suite with CocoDoc

Like using G Suite for your work to complete a form? You can do PDF editing in Google Drive with CocoDoc, so you can fill out your PDF to get job done in a minute.

  • Go to Google Workspace Marketplace, search and install CocoDoc for Google Drive add-on.
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PDF Editor FAQ

If a circle is enclosed by a sector and A, B and C are touching the circle, what is the ratio between the area of sector and area of circle?

See the figure below:Let the radius of the smaller circle be r.I will try to find out the radius of the bigger circle in terms of r.Then we are done.We can say from the figure that radius of bigger circle = OC.For this, we first need to prove that O, O1 and C are col-linear points.This can be proved if we can prove that:[math]\angle AO1O [/math][math][/math][math]+ \angle AO1C = 180^\circ [/math][math][/math][math]\\ From [/math][math][/math][math]\ right [/math][math][/math][math]\ angled [/math][math][/math][math]\ \bigtriangleup O1AO, [/math][math][/math][math]\\ [/math][math][/math][math]\ we [/math][math][/math][math]\ have \angle AO1O = 60^\circ. [/math][math][/math][math]\\ Now [/math][math][/math][math]\ concentrate [/math][math][/math][math]\ on\ \bigtriangleup AO1D. [/math][math][/math][math]\\ Its [/math][math][/math][math]\ a [/math][math][/math][math]\ isosceles [/math][math][/math][math]\ triangle. [/math][math][/math][math]\\ Since [/math][math][/math][math]\ AO1 = AO1 = r. [/math][math][/math][math]\\ Hence [/math][math][/math][math]\ \angle AD1O = \frac{(180 - \angle AO1D)}{2} [/math][math][/math][math]\\ = \frac{(180 - 60)}{2} = 60 [/math][math][/math][math]\\ [/math][math][/math][math] The [/math][math][/math][math]\ chord [/math][math][/math][math]\ AC [/math][math][/math][math]\ subtends [/math][math][/math][math]\ 60^\circ [/math][math][/math][math]. [/math][math][/math][math]\\ SO [/math][math][/math][math]\ it\ will [/math][math][/math][math]\ subtend [/math][math][/math][math]\ an [/math][math][/math][math]\ angle [/math][math][/math][math]\ of [/math][math][/math][math]\ 2*60^\circ [/math][math][/math][math]\ at [/math][math][/math][math]\ center. [/math][math][/math][math]\\ Hence [/math][math][/math][math]\ \angle AO1C = 120^\circ. [/math][math][/math][math]\\ So [/math][math][/math][math]\ we [/math][math][/math][math]\ have [/math][math][/math][math]\ [/math][math][/math][math]: [/math][math][/math][math]\\ \angle AO1O [/math][math][/math][math]+ \angle AO1C =\ 60^\circ [/math][math][/math][math]+ 120^\circ =\ 180^\circ [/math][math][/math][math]\\ \text{Hence the points O, O1 and C are col-linear.} [/math][math][/math][math]\\ So [/math][math][/math][math]\ radius [/math][math][/math][math]\ of [/math][math][/math][math]\ bigger [/math][math][/math][math]\ circle [/math][math][/math][math]\\ = OO1 [/math][math][/math][math]+ O1C. [/math][math][/math][math]\\ From [/math][math][/math][math]\ right [/math][math][/math][math]\ angled [/math][math][/math][math]\ \bigtriangleup AO1O, [/math][math][/math][math]\\ we [/math][math][/math][math]\ have: [/math][math][/math][math]\ \sin 30 = \frac{O1A}{O1O} [/math][math][/math][math]\\ => \sin 30 [/math][math][/math][math]\ = [/math][math][/math][math]\ \frac{r}{O1O} [/math][math][/math][math]\\ => O1O [/math][math][/math][math]\ = [/math][math][/math][math]\ \frac{r}{\sin 30} [/math][math][/math][math]\\ => O1O [/math][math][/math][math]\ = [/math][math][/math][math]\ 2r [/math][math][/math][math].\\ [/math][math][/math][math] Also\ O1C = r [/math][math][/math][math].\\ \text{So radius of bigger circle} = [/math][math][/math][math]\ OO1 [/math][math][/math][math]+ O1C = [/math][math][/math][math]\ 2r [/math][math][/math][math]+ r = 3r. [/math][math][/math][math]\\ [/math][math][/math][math] \frac{\text{Area of sector}}{Area of circle}\\ = \frac{\frac{\pi \cdot (3r)^2}{6}}{\pi\cdot r^2} [/math][math][/math][math]\\ [/math][math][/math][math] = \frac{3}{2}[/math]

What is the area of intersection of 2 circles of radius 5.5 cm whose centers are 6 cm apart?

For finding the area of the intersection of 2 circles, we may calculate the area of segment ABP & then double it, as the radius of both the circles are equal. Also O1O2 & AB will be perpendicular bisector of each other & AO1BO2 will be a rhombus.Since O1O2 = 6cm So, O1C = CO2 = 3cm angleSO1B= βNow, area of segment ABP = ar(sectorAO1BP) - ar( triangleAO1B)Area of sector = ( sector angle/ 360° ) pi r²Area of sector = (β/ 360°) (5.5)²pi ………….(1)Now area ( triangle O1BA) = .5*AB*3=> ar(tri O1BA) = 1.5AB = 1.5*2AC=> ar(tri O1 BA) = 1.5*2*√(5.5² -3²) = 3*8.5*2.5=> ar(triO1BA) = 63.75 ……….(2)Eq (1) - Eq(2) =Area of segment = [(β/360°) 30.25pi — 63.75]So, area of the intersection= 2* β/360° * 30.25pi - 63.75= [β/180° * 30.25pi - 63.75 ] cm² ………..ANS

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