Question

The triangle PQR is inscribed in the circle x2 + y2 = 25. If Q = (3, 4) and R=(-4, 3) then angle QPR=​

Answer 1

Answer:

The given equation of circle is x

2

+y

2

=25

∴ Centre is (0,0) and r=5

Now,

OR=

(−4−3)

2

+(3−4)

2

=

49+1

=

50

=5

2

units

OQ=OR=5 units

cos∠QOR=

2OQ×OR

OQ

2

+OR

2

−QR

2

⇒cos∠QOR=

2×5×5

25+25−50

=0

⇒∠QOR=90

o

We know the angle subtended by an arc at the centre is double the angle subtended by same arc at any point on the circle.

Now, ∠QOR=2∠QPR

⇒90

o

=2∠QPR

⇒∠QPR=45

o

=

4

π

.