Intersecting Chords Statements
CMAT 2024 · Quantitative Techniques & Data Interpretation · Medium · Geometry
Given below are two statements : Statement I: If two chords XY and ZT of a circle intersects internally at point P, then PX - PY = PZ - PT Statement II: If two chords XY and ZT of a circle intersect internally at point P, then PXZ and PTY are similar triangles. In the light of the above statements, choose the correct answer from the options given below:
- A.
Both Statement I and Statement II are true
- B.
Both Statement I and Statement II are false
- C.
Statement I is true but Statement II is false
- D.
Statement I is false but Statement II is true
D
Explanation
Statement I is false because the intersecting chords theorem states that , not subtraction. Statement II is true because (vertically opposite) and (angles in the same segment), making by AA similarity criterion.
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