In a triangle `A B C` , `N` is a point on `A C` such that `B N_|_A C` . If `B N^2=A N N C` , prove that `/_B=90o` .

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^@ .

In a triangle A B C , if A B=A C\ a n d\ A B is produced to D such that B D=B C , find /_A C D\ :\ /_A D C

In a triangle \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M || B C . Prove that: a r\ (triangle \ L O B)=a r\ (triangle \ M O C)

In Figure, A B C\ a n d\ D B C are two triangles on the same base B C such that A B=A C\ a n d\ D B=D Cdot Prove that /_A B D=/_A C D

A B C is a triangle in which A B=A C\ a n d\ P is a point on A C . Through C a line is drawn to intersect B P produced at Q such that /_A B Q=\ /_A C Q . Prove that: /_A Q C=90^@+1/2/_B A C

In Figure, A B C\ a n d\ D B C are two isosceles triangles on the same base B C such that A B=A C\ a n d\ D B=C Ddot Prove that /_A B D=\ /_A C D

If an a triangle A B C , b=3 c, a n d C-B=90^0, then find the value of tanB

If an a triangle A B C , b=3 c, a n d C-B=90^0, then find the value of tanB

In a triangle A B C ,\ /_A B C=\ /_A C B and the bisectors of /_A B C\ a n d\ /_A C B intersect at O such that /_B O C=120^0dot Show that /_A=/_B=/_C=60^0 .

In Figure, A B C is a right triangle right angled at B and D is the foot of the the perpendicular drawn from B on A C . If D M_|_B C and D N_|_A B , prove that: (i) D M^2=D NxxM C (ii) D N^2=D MxxA N