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An isosceles triangle ABC, with AB = AC,...

An isosceles triangle ABC, with AB = AC, circumscribes a circle, touching BC at P, AC at Q and AB at R. Prove that the contact point P bisects BC.

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Knowledge Check

  • ABC is an isosceles triangle with AB = AC. A circle through B touching AC at the middle point intersects AB at P. Then AP : AB is :

    A
    `4 :1`
    B
    `2:3`
    C
    `3:5`
    D
    `1:4`

  • ABC is an isosceles triangle with AB = AC. A circle through B touching AC at the middle point intersects AB at P. Then, AP : AB is

    A
    ` 3 : 5`
    B
    `1 : 4`
    C
    `4 : 1`
    D
    `2 : 3`

  • ABC is an isosceles triangle with AB = AC. A circle through B touching AC at the middle point Intersects AB at P. Then AP: AB is :

    A
    `4:1`
    B
    `2:3`
    C
    `3:5`
    D
    `1:4 `

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    Explore conceptually related problems

    A triangle ABC is drawn to circumscribe a circle. If AB = 13 cm, BC = 14 cm and AE =7 cm, then find AC.

    The bisector of /_B of an isosceles triangle ABC with AB=AC meets the circumcircle of ABC at P as shown in Figure.If AP and BC produced meet at Q, prove that CQ=CA

    The incircle of an isoceles triangle ABC, with AB=AC, touches the sides AB,BC and CA at D,E and F respecrively. Prove that E bisects BC.

    In Delta ABC, AB = AC. A circle is drawn with diameter AB and it intersects BC at D. Prove that D is the midpoint of BC.

    ABC is an isosceles triangle (AB = AC) circumscribed about a circle. Then, which of the following statements is correct ?

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