Home
Class 9
MATHS
P is any point in the angle ABC such tha...

P is any point in the angle ABC such that the perpendiculars drawn from P on AB and BC are equal. Prove that BP bisects angle ABC.

Answer

Step by step text solution for P is any point in the angle ABC such that the perpendiculars drawn from P on AB and BC are equal. Prove that BP bisects angle ABC. by MATHS experts to help you in doubts & scoring excellent marks in Class 9 exams.

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • TRIANGLES

    NAGEEN PRAKASHAN|Exercise Revision Exercise (long Answer Type Question)|8 Videos

  • TRIANGLES

    NAGEEN PRAKASHAN|Exercise Revision Exercise (very Short Answer Questions)|10 Videos

  • SURFACE AREA AND VOLUME

    NAGEEN PRAKASHAN|Exercise Revision Exercise (long Answer Questions)|10 Videos

Similar Questions

Explore conceptually related problems

ABC is a triangle and D is the mid-point of BC .The perpendiculars from D to AB and AC are equal.Prove that the triangle is isosceles.

The vertices of a triangle ABC are the points (0, b), (-a, 0), (a, 0) . Find the locus of a point P which moves inside the triangle such that the product of perpendiculars from P to AB and AC is equal to the square of the perpendicular to BC .

Knowledge Check

  • An isosceles triangle ABC is right angled at B.D is a point inside the triangle ABC. P and Q are the feet of the perpendiculars drawn from D on the sides AB and AC respectively of Delta ABC . If AP = a cm, AQ = b cm and angle BAD= 15^(@), sin 75^(@)=

    A
    `(2b)/(sqrt(3a))`
    B
    `(a)/(2b)`
    C
    `sqrt((3)(a))/(2b)`
    D
    `(2a)/(sqrt(3b))`

  • ABC is a triangle right angled at Aand a perpendicular AD is drawn on the hypotenuse BC. What is BC.AD equal to ?

    A
    AB .AC
    B
    AB . AD
    C
    CA .CD
    D
    AD . DB

  • ABC Is a right angled triangle, Night angled at C and p is the length of the perpendicular from Con AB. If a, b and c are the length of the sides BC, CA and AB respectively, then

    A
    `1/(p^2) = 1/(b^2) - 1/(a^2)`
    B
    `1/(p^2) = 1/(a^2) + 1/(b^2)`
    C
    `1/(p^2) + 1/(a^2) = -1/(b^2)`
    D
    `1/(p^2) = 1/(a^2) - 1/(b^2)`

    • Similar Questions

    Explore conceptually related problems

    BD is the disector of angle ABC. From a point P in BD, perpendiculars PE and PF are drawn to AB and BC respectively, prove that : (i) Triangle BEP is conguent to triangle BFP (ii) PE=PF.

    From a point O inside a triangle ABC , perpendiculars OD,OE and Of are drawn to rthe sides BC,CA and AB, respecrtively. Prove that the perpendiculars from A,B, and C to the sides EF, FD and DE are concurrent.

    ABC is a triangle right angled at C. Let p be the length of the perpendicular drawn from C on AB. If BC = 6 cm and CA = 8 cm, then what is the value of p ?

    P is a point inside a Delta ABC, D, E, F are the feet or perpendicular from P to the line BC, AB respectively. Show that (BC)/(PD)+ (CA)/(PE) + (AB)/(PF) ge (2s ^(2))/(Delta). Prove that equality holds if P is its incentre, s = semipermeter, Delta = area of triangle.

    let ABC be a triangle with AB=AC. If D is the mid-point of BC, E the foot of the perpendicular drawn from D to AC,F is the mid-point of DE.Prove that AF is perpendicular to BE.

    Home
    Profile