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Question

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= _______.


  1. 5DPB.

  2. 2DPB.

  3. 8DPB.

  4. DPB.


Solution

The correct option is D

DPB.


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.

PAB=BPS           ....(i)

(Angles in alternate segment)

Similarly we can prove that

PCD=DPS      .....(ii)

Subtracting (i) and (ii), we get

PCDPAB=DPSBPS

But in ΔPAC

Ext. PCD=PAB+CPA

PAB+CPAPAB=DPSBPS

CPA=DPB

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