   # In the figure if AC is a common tangent of two touching circles. If B is touching point of both circles...

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In the figure if AC is a common tangent of two touching circles. If B is the touching point of both circles then which is of the following is true about it and why...

1. Angle B is a right angle
2. Angle B is an obtuse angle
3. Angle B is an acute angle
4. There is not enough information to know anything about Angle B.  posted Nov 16, 2015

+1 vote

Suppose O1 is center of small circle and O2 of bigger one. Now O1 A is perpendicular at A on AC and O2C is perpendicular at C on the tangent AC. If I join O1 O2 then angle O1AC = angle O1AB + angle BAC = 90. Similarly, angle O2CA = angle O2CB + angle BCA.
This means angle B = angle A + angle C so B is 90. answer Nov 17, 2015

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In the figure AC is a common tangent of two touching circles. If B is touching point of both circles then find angle B. I have 3 unit circles. Two of them are externally tangent to each other. The third one passes through the tangent point, cutting two symmetrical areas from those two circles, as shown in the diagram. What is the shaded area? Three circles of equal radii all intersect at a single point P. Let the other intersections be A, B and C. Which of the following must be true?

a) P is the incentre of Triangle ABC
b) P is the circumcentre of Triangle ABC
c) P is the centroid of Triangle ABC
d) P is the orthocenter of Triangle ABC   