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Circles — Maths STD 9 — Question

CBSE BoardEnglish MediumSTD 9MathsCircles4 Marks
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Answer



Join chords AP and DQ.
For chord AP,
$\angle\text{PBA}=\angle\text{ACP}$ (Angles in the same segment) ...(1)
For chord DQ,
$\angle\text{DBQ}=\angle\text{QCD}$ (Angles in the same segment) ...(2)
ABD and PBQ are line segments intersecting at B.
$\therefore\angle\text{PBA}=\angle\text{DBQ}$ (Vertically opposite angles) ...(3)
From equations (1), (2), and (3), we obtain
$\angle\text{ACP}=\angle\text{QCD}$

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