question_answer

Consider the following statements in respect of two chords XY and ZT of a circle intersecting at P.

\[\mathbf{PZ}.\mathbf{PY}=\mathbf{PZ}.\mathbf{PT}\]

PXZ and PTY are similar triangles.

Which of the statements given above is/are correct?

A)  Only (i)                        

B)  Only (ii)         

C)  Both (i) and (ii)  

D)  None

Correct Answer: C

Solution :

(c): When two chords of a circle are intersect internally, then they are divided in a proportion. i.e.,   \[PX.PY=PZ.PT\] In    \[\Delta PXZ\] and \[\Delta PTY\], \[\angle ZPX=\angle YPT\]      (Vertically opposite angles) \[\angle PZX=\angle PYT\]      (Angles in same segment) \[\angle PXZ=\angle PTY\]      (Angles in same segment) \[\Delta PXZ=\Delta PTY\] Hence, the both statements are correct,