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# Calculate the area of the shaded region watch

1. Hello,

I'm stuck on a question in the C2 book (Edexcel). It's PG 97, EX 6C, Q 9.

In the diagram, AB and AC are tangents to a circle, centre 0 and radius 3.6cm (BO). Calculate the area of the shaded region, given that (Angle) BOC = 2/3pi radians.

Thank you.
Attachment 618534

---Moved to Maths---
2. (Original post by Edzinga)
Hello,

I'm stuck on a question in the C2 book (Edexcel). It's PG 97, EX 6C, Q 9.

In the diagram, AB and AC are tangents to a circle, centre 0 and radius 3.6cm (BO). Calculate the area of the shaded region, given that (Angle) BOC = 2/3pi radians.

Thank you.

---Moved to Maths---

3. The radius of a circle always meets the tangent at a 90 degree angle...

Consider cutting the kite in two to form two identical right-angled triangles...

You should be able to find the area of the shaded region from there (I think)

Ages since I did GCSE maths so apologies if this is wrong

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4. [QUOTE=TheMightyAugur;70026592]The radius of a circle always meets the tangent at a 90 degree angle...

Consider cutting the kite in two to form two identical right-angled triangles...

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Okay, Thank you. I'll try that and see where I get to.
5. (Original post by Edzinga)
The radius of a circle always meets the tangent at a 90 degree angle...

Consider cutting the kite in two to form two identical right-angled triangles...

-------------------------------------------------------------------------------------------------------

Okay, Thank you. I'll try that and see where I get to.
Did you try this? I noticed you created another thread but it was the same question so keep it all in this thread please.

You need to draw a horizontal line in the kite to split it into two triangles. Both triangles are right-angled because of a circle theorem (tangent/radius).

The picture isn't showing for me anymore so I can't be more specific with which two triangles I'm talking about.
6. (Original post by notnek)
Did you try this? I noticed you created another thread but it was the same question so keep it all in this thread please.

You need to draw a horizontal line in the kite to split it into two triangles. Both triangles are right-angled because of a circle theorem (tangent/radius).

The picture isn't showing for me anymore so I can't be more specific with which two triangles I'm talking about.
I've done the horizontal line and I've found the area of the kite as a whole, however I'm not sure how to find the area of the shaded region with this information

7. (Original post by Edzinga)
I've done the horizontal line and I've found the area of the kite as a whole, however I'm not sure how to find the area of the shaded region with this information
The shaded region is the area of the kite minus the area of the sector. Can you see that?

So the next step is to find the area of the sector.
8. (Original post by notnek)
The shaded region is the area of the kite minus the area of the sector. Can you see that?

So the next step is to find the area of the sector.
Ohhh okay, that's so much more obvious now you've pointed that out. Thank you very much.

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