Euclidean geometry: aadvanced rider

AI Thread Summary
LPN is a tangent to circle ADP, while circle BCP touches the larger circle internally at point P. The discussion involves applying the tangent-chord theorem to establish relationships between angles formed by the tangents and chords. It is noted that angles PBC and PCB are equal, leading to the conclusion that lines LN and AD are parallel, suggesting that angle PAD is also equal to the same measurement. The participant expresses uncertainty about their interpretation of the problem and requests further clarification to refine their solution.
VictoriaV
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Homework Statement



LPN is a tangent to circle ADP. Circle BCP touches the larger circle internally at P. Chord AD cuts the smaller circle at B and C and BP and CP are joined

Homework Equations





The Attempt at a Solution


∠P4+5 = ∠B1 (tan chord theorem)
∠P1+2 = C1 (tan chord theorem)
 

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The attached file shows the numbers 1 through 5 which I am taking to indicate that angles PBC, PCB, and LPA are all equal. You didn't say what the problem was.

I do notice:
Since angles PBC and PCB are equal and line LN is tangent at P, lines LN and AD are parallel.
That makes angle PAD also measurement #1.
That would mean that the two circles are identical.
So angles 2 and 4 are zero degrees.

I'm guessing that I have misinterpreted something.

If you provide details, I take another shot at it.
 

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