# In the given figure , if AOD = 135 then BOC is equal to what a)52.5 b)45 c)62.5 d)24

2
by SweetRohan

2015-02-15T18:31:42+05:30
It is 45 as aod+boc=180 as it is a known theorm
sir kvn murthy please solve my doubts i am waiting
you left me
2015-02-15T18:49:27+05:30

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Mark the angles a, x and y.  Then find the other angles, because we have right angle triangles.  Also we have identical triangles, as the sides are tangents from A , B C and D  on to the circle.   So the lengths of tangent segments on to the circle are equal.   Thus the angles inside the two adjacent triangles are equal.

Sum of all angles at the center = 360 deg

135-a + 135-a + a + a + 2 x + 2 y = 360 deg

2x + 2y = 90 deg

x + y = 45 deg =  angle BOC.