MathDB

A circumscribed pyramid

ABCDS

is given. The opposite sidelines of its base meet at points

P

and

Q

in such a way that

A

and

B

lie on segments

PD

and

PC

respectively. The inscribed sphere touches faces

ABS

and

BCS

at points

K

and

L

. Prove that if

PK

and

QL

are complanar then the touching point of the sphere with the base lies on

BD

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