Home
Class 10
MATHS
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 `angleADC=angleBAC` . Show `CA^(2)=CB.CD`

Text Solution

Verified by Experts

The correct Answer is:
`CA^(2) = CB xx CD`
Promotional Banner

Topper's Solved these Questions

  • TRIANGLES

    CPC CAMBRIDGE PUBLICATION|Exercise Exercise 2.4|9 Videos

  • TRIANGLES

    CPC CAMBRIDGE PUBLICATION|Exercise Exercise 2.5|17 Videos

  • TRIANGLES

    CPC CAMBRIDGE PUBLICATION|Exercise Exercise 2.2|10 Videos

  • SURFACE AREAS AND VOLUMES

    CPC CAMBRIDGE PUBLICATION|Exercise EXERCISE 15.4|5 Videos

Similar Questions

Explore conceptually related problems

In the given fig DeltaDGH~DeltaDEF, DH=8cm, DF=12cm, DG=(3x-1) cm and DE=(4x+2) cm, Find the lengths of DG and DE. OR D is a point on the side BC of DeltaABC such that lfloorADC=lfloorBAC . Prove that (CA)/(CD)=(CB)/(CA) .

If D, E and F are three points on the sides BC, CA and AB, respectively, of a triangle ABC such that the lines AD, BE and CF are concurrent, then show that " "(BD)/(CD)*(CE)/(AE)*(AF)/(BF)=-1

In Fig. 2.54, o is a point in the interior of a triangle ABC,ODbotBC,OEbotACandofbotAB. Show that AF^(2)+BD^(2)+CE^(2)=AE^(2)+CD^(2)+BF^(2).

D and E are points on sides AB and AC respectively of tirangle ABC such that ar (DBC) = ar (EBC) . Prove that DE || BC

If D is the mid-point of side BC of a triangle ABC and AD is perpendicular to AC, then

D and E are points on the sides CA and CB respectively of a triangle ABC right angale at C. prove that AE^(2)+BD^(2)=AB^(2)+DE^(2).

In Fig .D is a point on side BC of DeltaABC such that (BD)/(CD) =(AB)/(AC) prove that AD is the bisector of angleBAC.

D,E and F are respectively the mid-points of the sides BC, CA and AB of triangle ABC show that (i) BDEF is a parallelogram. (ii) ar (DEF) = 1/4 ar (ABC) (iii) ar (BDEF) = 1/2 ar (ABC)

In Fig E is a point on side CB produced of an isosceles triangle ABC with AB=AC. If ADbotBCandEFbotAC , prove that DeltaABD ~DeltaECT