If A B C and A M P are two right tr...

If ` A B C` and ` A M P` are two right triangles, right angled at `B` and `M` respectively such that `/_M A P=/_B A C` . Prove that ` A B C A M P` (ii) `(C A)/(P A)=(B C)/(M P)`

Topper's Solved these Questions

SURFACE AREAS AND VOLUMES
RD SHARMA|Exercise All Questions|417 Videos
TRIGONOMETRIC IDENTITIES
RD SHARMA|Exercise All Questions|254 Videos

Similar Questions

Explore conceptually related problems

In figure ABC and AMP are two right triangles, right angles at B and M respectively. Prove that(i) DeltaA B C~ DeltaA M P (ii) (C A)/(P A)=(B C)/(M P)

The points A(4, 7), B(p, 3) and C(7, 3) are the vertices of a right triangle, right-angled at B. Find the value of p.

In a A B C , P and Q are point on the sides A B and A C respectively, such that P Q B C . If A P=2. 4 c m , A Q=2c m , Q C=3c m and B C=6c m , find A B and P Q .

In A B C , P and Q are points on sides A B and A C respectively such that P Q B C . If A P=4c m ,\ \ P B=6c m and P Q=3c m , determine B C .

If AD and PM are medians of triangles ABC and PQR, respectively whereDeltaA B C DeltaP Q R , prove that (A B)/(P Q)=(A D)/(P M)

In A B C , points P and Q are on C A and C B , respectively such that C A=16 c m , C P=10 c m , C B=30 c m and C Q=25 c m . Is P Q ||A B ?

In Fig. 10.97, the sides A B ,\ B C and C A of triangle A B C , touch a circle at P ,\ Q and R respectively. If P A=4c m , B P=3c m and A C=11 c m , then length of B C is (FIGURE) (a) 11cm (b) 10cm (c) 14cm (d) 15cm

In P Q R , M and N are points on sides P Q and P R respectively such that P M=15 c m and N R=8c m . If P Q=25 c m and P R=20 c m state whether M N Q R .

In Figure, A B C is an isosceles triangle in which A B=A CdotC P A B and A P is the bisector of exterior /_C A D of A B C . Prove that /_P A C=/_B C A and (ii) A B C P is a parallelogram.

P and Q are points on sides A B and A C respectively of A B C . If A P=3c m , P B=6c m , A Q=5c m and Q C=10 c m , show that B C=3\ P Q .

RD SHARMA-TRIANGLES-All Questions

In an isosceles A B C , the base A B is produced both the ways ...
Text Solution
|
Diagonals A C and B D of a trapezium A B C D with A B D C intersec...
Text Solution
|
If A B C and A M P are two right triangles, right angled at B and...
Text Solution
|
A vertical stick of length 6m casts a shadow 4m long on the ground a...
Text Solution
|
In Fig. 4.145 (a) A B C is right angled at C and D E|A B . Prov...
Text Solution
|
If A B C D E F such that A B=1. 2 c m and D E=1. 4 c m . Find the ...
Text Solution
|
In two similar triangles A B C and P Q R , if their correspondin...
Text Solution
|
If A B C D E F such that area of A B C is 9\ c m^2 and the a...
Text Solution
|
In Fig. 4.166, P B and Q A are perpendiculars to segment A Bdot ...
Text Solution
|
Prove that the area of the equilateral triangle described on the si...
Text Solution
|
In Fig. 4.170, A B C D is a trapezium in which A B D C and A B=...
Text Solution
|
D ,\ E ,\ F are the mid-points of the sides B C ,\ C A and A B resp...
Text Solution
|
D and E are points on the sides A B and A C respectively of a A...
Text Solution
|
Two isosceles triangles have equal vertical angles and their areas ...
Text Solution
|
In Fig. 4.176, X Y A C and X Y divides triangular region A B C ...
Text Solution
|
Triangles A B C and D E F are similar. If area ( A B C)=16\ c m^2 ,...
Text Solution
|
Triangles A B C and D E F are similar. If area ( A B C)=36\ c m^2 ,...
Text Solution
|
In Fig. 4.177, A C B A P Q . If B C=10 c m , P Q=5c m , B A=6. 5...
Text Solution
|
The areas of two similar triangles are 81\ c m^2 and 49\ c m^2 resp...
Text Solution
|
The areas of two similar triangles are 169\ c m^2 and 121\ c m^2 re...
Text Solution
|