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Raja Sharma

· started a discussion

· 1 Months ago

geom (Question:111651.0)

sir pls provide video solution

Question:

ABCD is a cyclic quadrilateral. The tangents at A and C meet at a point P. If \(\angle\)ABC = 100°, then the value of the \(\angle\)APC will be:

Options:
A) 20°
B) 40°
C) 60°
D) 80°
Solution:
Ans: (a)


Since ABCD is a cyclic quadrilateral

\(\therefore \) \(\angle \)ADC = 180° -  \(\angle \)ABC

= 180° - 100° = 80°

also, \(\angle \)AOC = 2  \(\angle \)ADC

= 2 \(\times\) 80° = 160°

Now, \(\angle \)OAP = \(\angle \)OCP = 90°

Because we Know Radius and tangent intersect to each other at angle 90o .


From quadrilateral APCO, 

\(\angle \)OAP + \(\angle \)OCP + \(\angle \)AOC + \(\angle \)APC= 360°

90° + 90° + 160° + \(\angle \)APC = 360°

or \(\angle \)APC= 20°

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