Friday, December 25, 2009

Math Quiz IX - One Challenging Question!




The figure shows isosceles triangle ABC,
AB = AC, and with its incircle of radius 3 cm.
If the base is 8 cm, find the length of AB.






Hints :
1) This question can be solved using quadratic equations or better still, trigo
2) The center of the incircle is the point where the bisectors of the vertex angles meet
3) In the circle shown, the 3 sides of the triangle are tangents to the incircle
4) Tangent segments drawn from each vertex to the circle are equal, i.e. BP = BQ and AP= AR
5) The lines joining the incentre to the sides of the triangles at the points of contact are perpendicular to the sides of the triangles




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