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Great circles question

This topic has 2 member replies
mihai9 Junior | Next Rank: 30 Posts Default Avatar
Joined
08 Nov 2017
Posted:
19 messages

Great circles question

Post Fri Dec 22, 2017 10:29 am
There are three points O, P, Q, O is the center of the circle, P and Q are two points on the circle, and ∠POQ is 45 °, then it seems that the area of a triangle is 12, Find the area of a circle ?

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thucanh711 Newbie | Next Rank: 10 Posts
Joined
23 Dec 2017
Posted:
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Post Sun Jan 07, 2018 3:15 am
Hi there,
hope my explanation could help you.

As O is the center of the circle and P, Q are on the circle => OP = OQ = r (the radius of the circle)

The area of the triangle can be calculated by: S = 1/2 sin($$\angle$$ POQ) OP. OQ = 1/2 . $$\frac{\sqrt{2}}{2}$$ . OP . OQ

We have S = 12 => the value of OP.OQ

OP.OQ = r. r = $$r^2$$

The area of the circle: S' = $$\pi.r^2$$

You can get your answer now.

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DrMaths Senior | Next Rank: 100 Posts Default Avatar
Joined
15 Jan 2018
Posted:
82 messages
Post Thu Feb 01, 2018 8:22 am
8 of these triangles will make an octagon, whose area is 2√2r^2
So 2√2r^2 = 8 * 12
√2r^2 = 48
r^2 = 24√2

Area of circle = pi * r^2 = pi * 24√2

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