2026 · Q64
ABCD is a cyclic quadrilateral. AB and DC are produced to meet at P. Which of the following statements is/are correct?
- IΔPAD is similar to ΔPBC.
- II∠PAD + ∠PDA = ∠PBC + ∠PCB. Select the answer using the code given below:
Elementary MathematicsQuadrilaterals and Polygons
- AI only
- BII only
- CBoth I and II
- DNeither I nor II
Explanation
∠P is common; cyclicity gives ∠PAD=180°−∠BAD=∠BCD=∠PCB and ∠PDA=∠PBC. Hence ΔPAD is similar to ΔPCB, but the stated correspondence ΔPAD~ΔPBC mis-matches the vertices, so I is false on the strict reading. Statement II follows directly from those angle equalities, so it is true. Only II is correct, option B.