In the given figure O is the centre of the circle and angle DCE 45 if CD 10 radic 2cm then what...........

Quantitative Aptitude (CGL) Coordinate Geometry

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In the given figure O is the centre of the circle and angle DCE=45. if CD=10√2cm, then what is the lenth of AC? (CB=BD)

15.5

18.5

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Explanation:

Now we have < DCE = 45°
< OCB = 45°
hence we can say ? OBC is a right angle isosceles triangle means BC = OB = 10√2 /2 cm = 5√2
in right angle isosceles triangle OBC we can have
OC² = BO²+ BC² ( By phythagoras theorem)
=> OC² =(5 √2 ) ²+ (5√2)²
=> OC² = 100 => OC= 10cm
OC= AB = 10cm ( OC= AB radius of same circle )
Now and right angle ? ABC we have
AC² = BC² + AB²
AC²= (5√2)² + (OB+ AO)²
AC² = 50+50 +2× 5 √2 ×10 +100
AC= √314.42 = 18.5 cm