Question

PQ and PR are the tangents to given circle as shown in the figure if. angle RPQ is equal to 90 degree and PQ is equal to 8 cm find radius of the circle

Answer 1

construction:-join OP
sol.:-
in triangle OPR

$tan45 = \frac{or}{rp}$
$1 = \frac{or}{8} \\ or = 8cm$

Answer 2

PQ and PR are the tangents drawn from the same point to the circle.
hence tangent theorem,
PQ = PR
PQ = PR = 8cm.
now, angle RPQ = 90°
OR and OQ are radius of circle.

tangent and radius are always perpendicular on the point on circle
hence,. angle ORP = angle OQP = 90°
angle QOR = 90° ...... remaining angle of quadrilateral.

here, all angles are 90° and one pair of adjecnt sides is equal.
hence given quadrilateral is a square.
then radius of circle is 8 cm