Question: The incenter of the triangle is at the point A(x1, y1). Q, Y(x2, y2) are two points on the sides of the triangle as shown. Find the distance between A and Q, if x1 = 3, y1 = 7, x2 = 6 and y2 = 3.
A ) 6.5 units B ) 5 units C ) 6 units D ) 8 units
Steps to derive
1 As ‘A’ is the incenter of the triangle, the points Q and Y are equidistant from A. [Incenter of a triangle is equidistant from its sides.]
2 Distance between A and Y = AY = (6-3)2+(3-7)2 = 25 [Use distance formula.]
3 Distance between A and Q = AQ = AY = 25
= 5 [AQ = AY.]
