D is a point on the side BC of a triangl...

D is a point on the side BC of a triangle ABC such that `/_A D C=/_B A C`. Show that `C A^2=C BdotC D`.

Topper's Solved these Questions

TRIANGLES
VK GLOBAL PUBLICATION|Exercise LONG ANSWER QUESTIONS|18 Videos
TRIANGLES
VK GLOBAL PUBLICATION|Exercise HOTS (High Order Thinking Skills)|7 Videos
TRIANGLES
VK GLOBAL PUBLICATION|Exercise SHORT ANSWER QUESTIONS-I|12 Videos
REAL NUMBERS
VK GLOBAL PUBLICATION|Exercise Self -Assessment Test|11 Videos
VALUE-BASED QUESTIONS
VK GLOBAL PUBLICATION|Exercise Unit-VII : (Statistics & Probability)|8 Videos

Similar Questions

Explore conceptually related problems

In figure D is a point on side BC of a DeltaA B C such that (B D)/(C D)=(A B)/(A C) . Prove that AD is the bisector of /_B A C .

In figure, O is a point in the interior of a triangle ABC, O D_|_B C ,O E_|_A C and O F_|_A B . Show that (i) O A^2+O B^2+O C^2-O D^2-O E^2-O F^2=A F^2+B D^2+C E^2 (ii) A F^2+B D^2+C E^2=A W^2+C D^2+B F^2

Triangles A B C and +DBC are on the same base B C with A, D on opposite side of line B C , such that a r(_|_ A B C)=a r( D B C)dot Show that B C bisects A Ddot

Let D be the middle point of the side BC of a triangle ABC. If the triangle ADC is equilateral, then a^(2) : b^(2) : c^(2) is equal to

In figure E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If A D_|_B C and E F_|_A C , prove that DeltaA B D ~DeltaE C F .

In a hat harr ABC,D and E are points on sides AB and AC respectively such that BD=CE. If /_B=/_C, show that DE|BC.

If D is the mid-point of the side BC of triangle ABC and AD is perpendicular to AC, then 3b^(2)=a^(2)-c( b )3a^(2)=b^(2)3c^(2)b^(2)=a^(2)-c^(2)(d)a^(2)+b^(2)=5c^(2)

In a scalene triangle A B C ,D is a point on the side A B such that C D^2=A D D B , sin s in A S in B=sin^2C/2 then prove that CD is internal bisector of /_Cdot

In Fig. 4.124, E is a point on side C B produced of an isosceles triangle A B C with A B=A C . If A D_|_B C and E F_|_A C , prove that (i) A B D E C F (ii) A BxxE F=A DxxE C . (FIGURE)

In Figure, A B C is a triangle in which /_B=2/_C . D is a point on side B C such that A D bisects /_B A C a n d A B=C DdotB E is the bisector of /_B . The measure of /_B A C is 72^0 (b) 73^0 (c) 74^0 (d) 96^0

VK GLOBAL PUBLICATION-TRIANGLES-SHORT ANSWER QUESTIONS-II

In Fig. 7.15,DE abs() OQ and Dfabs()OR,Show that Efabs()QR.
Text Solution
|
The line joining the mid-points of two sides of a triangle is parallel...
Text Solution
|
State which pairs of triangles in Figure are similar. Write the sim...
Text Solution
|
In Fig. 4.96, (A O)/(O C)=(B O)/(O D)=1/2 and A B=5c m . Find the ...
Text Solution
|
E is a point on the side AD produced of a parallelogram ABCD and BE i...
Text Solution
|
In the given figure, S and T are points on sides PR and QR of Delta PQ...
Text Solution
|
In figure ABC and AMP are two right triangles, right angles at B an...
Text Solution
|
D is a point on the side BC of a triangle ABC such that /A D C=/B A C....
Text Solution
|
ABC is an equilateral triangle of side 2a. Find each of its altitud...
Text Solution
|
An aeroplane leaves an airport and flies due north at a speed of 1000...
Text Solution
|
In the given figure, DeltaABC and DeltaDBC are on the same base BC. If...
Text Solution
|
In the given figure, PA, QB and RC each is perpendicular to AC such th...
Text Solution
|
In Fig. 7 .27, if DeltaABC~ DeltaDEF and their sides are oflengths (in...
Text Solution
|
In Delta ABC it is given that (AB)/(AC)=(BD)/(DC) . If angle B=70^(@) ...
Text Solution
|
If the diagonals of a quadrilateral divide each other proportionally, ...
Text Solution
|
In the given figure (PS)/(SQ)=(PT)/(TR) and anglePST = anglePRQ. Prove...
Text Solution
|
Diagonals of a trapezium ABCD with AB || DC intersect each other at...
Text Solution
|
In the given Fig. 7.32, find the value of x in terms of a, b and c.
Text Solution
|
In the given Fig. 7.33, Cdabs()LA and DEabs()AC. Find the length of CL...
Text Solution
|
In the given Fig. 7 .34, AB = AC. E is a point on CB produced. If AD i...
Text Solution
|