CO-ORDINATE geometry doubts

Please tell the approach …
I thought of assuming a variable point the line in terms of lambda …then using angle formula
tan@= |m1 - m2/1+m1m2|
we can differentiate it and find labmda then find distance and take ratio but it will be too lengthy and I’m unsure
Anyone has a better method ??

This was a nice problem @Achilles. Thanks for sharing. :grin:

Here’s the optimal condition.

I tried my level best explaining :joy:.

8 Likes

Now you can use family of circles to find the point of contact.

Bro awesome solution. :exploding_head:

1 Like

Thanks :blush:

1 Like

Similar problem

1 Like

Ok so I have given a proof for the thing unknowingly.:wink:

2 Likes

Herr. Rudra , it’s Genius

PS-
I may sound fool but is there any property of circle that angle at outside point is less than that of inside or on circle point.

Angle made by diameter at any point inside is greater than 90, on circle is 90, outside cirlce is less than 90

2 Likes

No i am not aware of such property but its logical. See triangle F1P1’F2 and imagine shifting P1’ outwards till it reaches P1. You can clearly visualise the angle is decreasing.
I drew that extra triangle to avoid this confusion.

4 Likes

thanks
@Lavesh
@Rudra_d

@Rudra_d’s answer in post #2 should be marked as solution honestly. @Achilles

2 Likes

I didn’t know that if i can mark only one answer as solved …
I marked both of yours as solved :sweat_smile:

1 Like

image
Ans:16

Koi batado kaise karna hai pl



Sorry for the late response dude :sweat_smile:

4 Likes

no worries i eventually got it :grinning_face_with_smiling_eyes:

3 Likes