Home
Class 10
MATHS
A B C is an isosceles triangle with A B=...

`A B C` is an isosceles triangle with `A B=A C` and `D` is a point on `A C` such that `B C^2=A CxC Ddot` Prove that `B D=B C`

Text Solution

AI Generated Solution

To solve the problem step by step, we will use the properties of isosceles triangles and the concept of similar triangles. ### Step-by-Step Solution: 1. **Identify the Given Information:** - Triangle ABC is isosceles with \( AB = AC \). - Point D is on line segment AC. - The relationship given is \( BC^2 = AC \cdot CD \). ...
Promotional Banner

Topper's Solved these Questions

  • TRIANGLES

    NAGEEN PRAKASHAN ENGLISH|Exercise Problems From NCERT/ Exemplar|14 Videos

  • TRIANGLES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 6a|24 Videos

  • STATISTICS

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise Long Answer Questions|4 Videos

  • VOLUME AND SURFACE AREA OF SOLIDS

    NAGEEN PRAKASHAN ENGLISH|Exercise Revisions Exercise Long Answer Questions|5 Videos

Similar Questions

Explore conceptually related problems

A B C is an isosceles triangle with A B=A C and D is a point on A C such that B C^2=A CXC D . Prove that B D=B C .

If A B C is an isosceles triangle and D is a point on B C such that A D_|_B C then,

In Figure, A C > A B\ a n d\ D is the point on A C such that A B=A Ddot Prove that B C > C D

In an isosceles triangle A B C with A B=A C and B D_|_A Cdot Prove that B D^2-C D^2=2C DdotA Ddot

A B C is a triangle in which A B=A C and D is any point in B C . Prove that A B^2-A D^2=B D C D .

\ ABC is an isosceles triangle with A B=A C . Side B A is produced to D such that A B=A D . Prove that /_B C D is a right angle.

In Figure, A B C is an isosceles triangle with A B=A C ,\ B D\ a n d\ C E are two medians of the triangle. Prove that B D=C E

A B C is a triangle in which /_B=2/_C. D is a point on B C such that A D bisects /_B A C\ a n d\ A B=C D . Prove that /_B A C=72^@ .

If A B C is an isosceles triangle such that A B=A C and A D is an altitude from A on B C . Prove that (i) /_B=/_C (ii) A D bisects B C (iii) A D bisects /_A

If A B C is an isosceles triangle such that A B=A C and A D is an altitude from A on B C . Prove that (i) /_B=/_C (ii) A D bisects B C (iii) A D bisects /_A