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    1. Triangle ABC is isosceles with AB = AC. Let the circle having diameter AB and centre O
    intersect BC at some point P. Find the ratio BP/BC.

    After drawing out a diagram how would I go about solving it? Could I just give the length of AB 2 and go from there?
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    (Original post by mathslover46456)
    1. Triangle ABC is isosceles with AB = AC. Let the circle having diameter AB and centre O
    intersect BC at some point P. Find the ratio BP/BC.

    After drawing out a diagram how would I go about solving it? Could I just give the length of AB 2 and go from there?
    What does your diagram look like??

    To begin I'd assign some variables such as \theta for the base angle of the triangle and d as the diameter, then proceed to express BP and BC in terms of these two variables.

    Do you have the answer to this question??
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    (Original post by mathslover46456)
    1. Triangle ABC is isosceles with AB = AC. Let the circle having diameter AB and centre O
    intersect BC at some point P. Find the ratio BP/BC.

    After drawing out a diagram how would I go about solving it? Could I just give the length of AB 2 and go from there?
    Ratio questions in geometry can often involve similar shapes since in similar shapes, the ratio of corresponding side lengths is equal

    Draw the line AP on your diagram and see if you can prove that triangle ACP is similar to triangle APB. Please post your working if you get stuck.
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    you can create a new triangle BOP which will be similar to ABC.AO=OB=OP which means that angleABC=angleBPO.
    That means that angles are the same in both triangles.
    Therefore ratio BP/BC=BO/BA
 
 
 
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