Match the following. Parent triangles are counted up to similarity in A. List I List II (A) Number of parent-triangle configurations for which an acute triangle ABC is the orthic (pedal) triangle. (P)

Question

Match the following. Parent triangles are counted up to similarity in A.

List I	List II
(A) Number of parent-triangle configurations for which an acute triangle ABC is the orthic (pedal) triangle.	(P) 3
(B) DEF is the orthic triangle of an acute triangle ABC; $R_{1}$ , $R_{2}$ are the circumradii of DEF,ABC. Find $R_{2}$ / $R_{1}$ .	(Q) 2
(C) D∈BC,E∈CA,F∈AB and AD,BE,CF are concurrent. Find BD·CE·AF/(DC·AE·FB).	(R) 4
(D) In right triangle ABC with A=90°, exradii at A,B,C are $r_{1}$ , $r_{2}$ , $r_{3}$ . Find (3/2)(1- $r_{1}$ / $r_{2}$ )(1- $r_{1}$ / $r_{3}$ ).	(S) 1
	(T) 5

Options:

Answer:

A

Solution:

An acute orthic triangle corresponds to one acute and three obtuse labeled parent configurations up to similarity, giving 4. Its circumradius is half its parent circumradius, giving 2 in B. Ceva gives C=1. In D, substitution of the right-triangle exradius formulas simplifies to 3.

TestHub · Accepted Answer

An acute orthic triangle corresponds to one acute and three obtuse labeled parent configurations up to similarity, giving 4. Its circumradius is half its parent circumradius, giving 2 in B. Ceva gives C=1. In D, substitution of the right-triangle exradius formulas simplifies to 3.

Mathematics - Properties of Triangle Question with Solution | TestHub

Options:

Doubts & Discussion