PS question (circle)

Question

Please, help with the attached question

subhen · Answer

PQ || OR, angle ORP=35 and OR=18 Therefore radius=9

Therefore angle RPQ=35 (since PQ || OR and ORP and RPQ are alternate angles)

Let C be the center of Circle.

Therefore angle OCP=70 (Centre angle OCP is twice its inscribed angle ORP)
For same reasons angle RCQ=70

angle PCQ + angle OCP + angle RCQ = 180
angle PCQ + 70 + 70 = 180
angle PCQ = 40

Therefore length of arc PQ = (40/360)18*pie=2*pie

abhi_ferrari · Answer

Subhen, can you please explain what is the inscribed angle for RCQ? Thanks.

subhen · Answer

angle RPQ is the inscribed angle for angle RCQ. Since RPQ is 35, hence RCQ is twice that i.e. 70.

Vlad77 · Answer

Thanks <img src="{SMILIES_PATH}/icon_biggrin.gif" alt=":-D" title="Very Happy" /> !!!

mohansb · Answer

Can you please attach the question.. I don't see that at all.

Sumithra Sen · Answer

I am very confused about inscribed angles here..

How can RCQ be Inscribed?

Any websites to understand Inscribed angles in better detail!

abhi_ferrari · Answer

Sumithra, even I had some difficulty visualizing the inscribed angle. Try thinking it this way - Focus on the minor arc QR. Try finding the following two angles. Angle that includes this arc with one vertex on the circumference of the circle (call it angle 1). The angle that includes this arc but with once vertex on the centre of the circle (call it angle 2). 

Angle 2 = 2*angle 1

Now try relooking at the figure of this question. It should be clear.

PS question (circle)

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