Question

11) In the figure, ABC is a triangle and O is a
point in it. OP and OQ are drawn
perpendicular to the sides AB and BC
respectively. If ZB = 65°, find ZPOQ
А
Р
O
65°
B
С
Q​

Answer 1

Answer:

SORRY MATE BUT THERE'S NO FIGURE ATTACHED!

Step-by-step explanation:

HOPEFULLY IT HELPS! PLEASE MARK AS BRAINLIEST!

Answer 2

Answer:

In △POU and △QOR

∠O=∠O (same angle)

∠P=∠Q [each 90

o

]

∴ △POU∼△QOR... (AA test of similarity)

∴

OQ

OP

=

QR

PV

−−−(1)

Also, in △UPT and △SQT

∠P=∠Q... {each 90

o

}

∠UTP=∠STQ.... (vertically opposite angles)

∴△UPT∼△STQ... (AA test of similarity)

∴

SQ

UP

=

QT

PT

but SQ=RQ... (Q is mid point)

∴

RQ

UP

=

QT

PT

.....(2)

∴ from (1) and (2)

QT

PT

=

OQ

OP

OQ−OT

OT−OP

=

OQ

OP

∴ OT.OQ−OQ.OP=OP.OQ−OP.OT

∴ (OQ).(OT)+(OP)(OT)=2(OP).(OQ)

∴ OT(OQ+OP)=2(OP).(OQ)

∴

(OP).(OQ)

OQ+OP

=

OT

2

∴

OP

1

+

OQ

1

=

OT

2

solution