Two chords AB and CD of a circle with centre O, intersect each other at P. If \[\angle AOD=100{}^\circ \] and \[\angle BOC=70{}^\circ ,\] then the value of \[\angle APC\] is [SSC (CGL) Mains 2014] |
A) \[80{}^\circ \]
B) \[75{}^\circ \]
C) \[85{}^\circ \]
D) \[95{}^\circ \]
Correct Answer: D
Solution :
(d) In the given figure,\[\angle AOD=100{}^\circ \]\[\Rightarrow \]\[\angle BOC=70{}^\circ \] |
Now, join AC. |
\[\angle ACD=\frac{1}{2}\angle AOD\] |
[since, angle subtended at the centre is twice the angle subtended on circumference of following circle] |
\[=\frac{1}{2}\times 100=50{}^\circ \] |
Similarly, \[\angle CAB=\frac{1}{2}\times \angle DOB=\frac{1}{2}\times 70{}^\circ =35{}^\circ \] |
In \[\Delta APC,\]\[\angle APC=180{}^\circ -\angle ACP-\angle CAB\] |
\[=180{}^\circ -50{}^\circ -35{}^\circ \]\[[\because \angle ACP=\angle ACD]\]\[=95{}^\circ \] |
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