Relationship of circles and polygons

[Ihatdogs10]

Hi good day can you help me prove this? This is my assignment for math subject 10

I think it is about their equality but It is just my guess.
Thank you

 

[Harry_the_cat]

Firstly, draw in the radii PX and QY, forming two triangles. What do you know about these two triangles?

 

[Ihatdogs10]

I don't have Idea about those 2 triangles

 

[JayJay]

Seems to be an error in the question. Should "QC" read "QO"

 

[Harry_the_cat]

Seems to be an error in the question. Should "QC" read "QO"

Yes QC should be QO

 

[Harry_the_cat]

Have you learnt any theorems about circles and tangents?

 

[Ihatdogs10]

I have 2 secants intersecting outside the circle? Am I right?

 

[Ihatdogs10]

But I dont know how to apply it to the given

 

[Harry_the_cat]

PQ is a tangent to both circles.
XY joins the centres of the circles.

 

[Harry_the_cat]

What do you know about the angle XPO?

 

[Ihatdogs10]

I don't have idea about that angle

 

[Harry_the_cat]

ok. Have you learnt any theorems regarding circles and tangents?

 

[Ihatdogs10]

secant tangent? or chord secant?

 

[Harry_the_cat]

Do you know what a tangent to a circle is?

 

[Ihatdogs10]

yes tangent is a line that intersect at one point and secant in 2 points in circle

 

[Ihatdogs10]

P is tangent I dont know O because I think it did not intersect in circle

 

[Harry_the_cat]

Good. Forget about the secant. So can you see that PQ is a tangent to both circles.

 

[Ihatdogs10]

x is a point

 

[Ihatdogs10]

yes

Good. Forget about the secant. So can you see that PQ is a tangent to both circles.

 

[Harry_the_cat]

P is not a tangent. P is a point. It is the point where the tangent PQ touches the big circle.