Two circles touch each other internally at a point P. A chord AB of the bigger circle intersects the other circle in C and D. Then, ∠CPA= _______.
Given - Two circles touch each other internally at P. A chord AB of the bigger circle, intersects the smaller circle at C and D, AP, BP, CP and DP are joined.
Construction - Draw a tangent TS at P to the circles given.
∵TPS is the tangent, PD is the chord.
(Angles in alternate segment)
Similarly we can prove that
Subtracting (i) and (ii), we get
But in ΔPAC