# Problem of a circle tangent to three other circles [closed]

Two circles with centres A and B and radii 14 and 7 units respectively touch each other externally. M is the mid point of segment DE and is the centre of the circle with radius 21 units. The two smaller circles touch the larger circle internally. A co ordinate system has been set up with the origin as M, and other points lie on the X-axis.

To find: The coordinates of the centre and radius of a circle and which touches the smaller circles externally and the larger circle internally.

Note: To be solved without using Apollonius problem and Descartes theorem.

Hints: Use Stewart's theorem and Pythagoras theorem

## closed as off-topic by heropup, Claude Leibovici, JonMark Perry, user91500, user99914 Feb 3 '16 at 10:48

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• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – heropup, Claude Leibovici, JonMark Perry, user91500, Community
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• Where does DE come into play? – Sawarnik May 15 '14 at 5:55
• And can you include a figure? – Sawarnik May 15 '14 at 6:06
• I've added a diagram according to my understanding of the problem; @Chinmay, if this is incorrect, please let us know. – user21467 May 16 '14 at 22:50
• If the figure, is in fact correct, the following video might have some ideas for an alternate solution: youtube.com/watch?v=sG_6nlMZ8f4 – Alice Ryhl May 16 '14 at 23:01