question_answer

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

1. PX\[\cdot \]PY=PZ\[\cdot \]PT

2. PXZ and PTY are similar triangles.

Which of the above statements is/are correct?

A) Only 1              

B) Only 2

C) Both 1 and 2/1  

D) Neither 1 nor 2

Correct Answer: C

Solution :

When two chords of a circle intersect internally, then they are divided in a proportion. i.e., PX. PY- PZ. PT On \[\Delta \]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) \[\therefore \]\[\Delta \]PXZ \[\sim \]\[\Delta \]PTY Hence, the both statements are correct.