The circle d circumscribes abc and abe. Which statements about triangles are true? statement i: the bisectors of abc intersect at the same point as those of abe. statement ii: the distance of cad is the same as the distance of da and e. statement iii: cde bisector. statement iv: the bisectors of abc intersect at the same point as those of abe. a. I come from b. i.e. ii c. ii and iv d. i.e. iii e. iii and iv
I and II Explanation step by step: Statement I: The bisectors of ABC intersect at the same point as those of ABE. Statement 1 is true because the bisectors intersect at the center of the circumcircle. As the two triangles have the same circumcircle, their bisectors therefore intersect at the same point. Therefore, statement I is true. Statement II: The distance from C to D is the same as the distance from D to E.
Since both, i.e. the distance from C to D and the distance from D to E represent the radius of the circle, hence both are of equal length. Therefore, only I and II are correct.
Il B Step-by-step explanation:
The correct option is; B. I and II Explanation step by step: Statement I: The bisectors of ABC intersect at the same point as those of ABE The above statement is correct because since ΔABC and ΔABE are inscribed in the circle with center D, their sides are equivalent or similar to tangent lines offset closer to the center of the circle, so that the bisectors of the sides of ΔABC and ΔABE are on the same path as a line joining the tangents at the center of the circle. sides of ΔABC and ΔABE will pass through the same point which is the center of circle D Statement II: The distance from C to D is the same as the distance from D to E The above statement is correct because D is the center of the circumcircle and D and E are points on the circumference such that the distances C to D and D to E are both equal to the radial length. Distance from C to D = Distance from D to E = Length of the radius of the circle with the center D Statement III: Bisect CDE The statement above may require more information Statement IV The bisectors of angle ABC intersect at same point as those of ABE The above statement is incorrect because the point of intersection of the bisectors of ΔABC and ΔABE are the respective centers found in the perimeter of ΔABC and ΔABE respectively and are therefore different points.