252 An example in illustration thereof. 211-212. The man who travels to the cast moves at the rate of 2 yöjunas (a day); and the other man who travels north- wards moves at the rate of 3 yojanas (a day). This (latter man) having thus moved on for 5 days turns to move along the hypo- tenuse. In how many days will he meet the (other) man ? Both (of them) move out at the same time, and the number of days spent (by both of them) in journeying out is the same. GANITASARASANGRAHA. The rule for arriving at the numerical value of the diameters of circles described about the eight kinds of figures consisting of the five kinds of quadrilateral figures and the three kinds of triangular figures (already mentioned) :- 213. In the case of a quadrilateral figure, the value of the diagonal (thereof), divided by that of the perpendicular, and (then) multiplied by that of the lateral side, gives rise to the value of the diameter of the circumscribed circle In the case of a trilateral figure, the product of the values of the two sides (other than the base) divided by the value of the perpendicular (gives rise to the required diameter of the circumscribed circle). Examples in illustration thereof. 214. In the case of an equilateral quadrilateral figure having 3 as the measure of each of (its) sides, and also in the case of another (quadrilateral figure) of which the vertical side measures 5 and the horizontal side measures 12, what is the measure (of the diameter) of the circumscribed circle? 213. Let ABC be a triangle inscribed in a cncle, AD the diamoter thereof, and BE the perpendicular on AC. Join BD. Now the triangles ABD and BEC are similar. .. AB. AD-BE BC AB x BC . AD BE This is the formula given in the rule A for the diameter of a circle circumscribed about a quadrilateral or a triangle. B D C
