Any good mathematicians, need help

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?

OP

@notnek any help?

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??

Reply 3

Notnek

21

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.

(edited 7 years ago)

Reply 4

anaxiedgi

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

(edited 6 years ago)

Reply 5

AbhinavKumar

1

use similarity, sketch a diagram, and then use the property of a semi circle wherein the angle of the triangle is 90. therefore triangles APB and APC are similar, therefore the sides are similar, therefore ratio is 1:1

Any good mathematicians, need help

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