Suppose BC is a given line segment in the pla | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the given scalene triangle $T$ have vertices $P, Q, R$. We want to find the number of points $A$ such that $	riangle ABC \sim 	riangle PQR$

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(C) Let the given scalene triangle $T$ have vertices $P, Q, R$. We want to find the number of points $A$ such that $	riangle ABC \sim 	riangle PQR$ with the vertices corresponding in the given order.For a fixed line segment $BC$ and a fixed triangle $T$ (with sides $p, q, r$),the similarity $	riangle ABC \sim 	riangle PQR$ implies that the ratio of sides $AB/PQ = BC/QR = AC/PR$ is fixed.For each ordered correspondence of the vertices of $	riangle ABC$ to the vertices of $	riangle PQR$,there are $2$ possible locations for point $A$ (one on each side of the line $BC$).Since there are $3! = 6$ possible permutations of the vertices $P, Q, R$ to match the vertices $A, B, C$ (or more precisely,$6$ ways to map the sides of $T$ to the segment $BC$),and for each mapping,there are $2$ possible positions for $A$ (one on either side of $BC$),the total number of points $A$ is $6 	imes 2 = 12$.

Suppose $BC$ is a given line segment in the plane and $T$ is a scalene triangle. The number of points $A$ in the plane such that the triangle with vertices $A, B, C$ (in that order) is similar to triangle $T$ is

Similar Questions

There are $3, 4,$ and $5$ points on the sides $AB, BC,$ and $CA$ of a triangle $ABC$ respectively. How many triangles can be formed using these points as vertices?

There are $6$ points on a circle. Two triangles are drawn such that they have no common vertices. What is the probability that none of the sides of the triangles intersect?

$A$ polygon has $44$ diagonals. Then the number of sides of the polygon is:

Out of $n$ points in a plane,$p$ points are collinear. (No three of the remaining points are collinear). The number of lines that can be drawn passing through these points is:

Suppose that $20$ pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars,then the total number of beams is

Vedclass Test Series

Exam Paper Generator

Online Exam Module