(iii) In the figure, O is the centre of the circle.
PQ and PR are tangents to the circle at
points Q and R respectively. If PQ = 7 cm
then what is the length of seg PR? Give
reason.
Answers
Answer:
7 cm
Step-by-step explanation:
PR = 7 cm
the length of tangent made from an external point to the circle are equal
proof
construct OP, OQ, and OR
OQ and OR are the radius of circle
OP is distance of external point to the centre of circle.
we get two right angle triangle
as the tangent make a right angle at the point of contact with the radius.
∆OPQ and ∆OPR
OQ = OR ( radius of circle)
OP = OP ( Common side)
angle OQP = angle ORP ( 90° tangent make 90° with the radius)
therefore the two triangle are congruent.
PQ = PR ( Corresponding sides of the congruent triangle)
PQ = PR = 7cm
hope you get your answer
Answer:PR = 7 cm
the length of tangent made from an external point to the circle are equal
proof
construct OP, OQ, and OR
OQ and OR are the radius of circle
OP is distance of external point to the centre of circle.
we get two right angle triangle
as the tangent make a right angle at the point of contact with the radius.
∆OPQ and ∆OPR
OQ = OR ( radius of circle)
OP = OP ( Common side)
angle OQP = angle ORP ( 90° tangent make 90° with the radius)
therefore the two triangle are congruent.
PQ = PR ( Corresponding sides of the congruent triangle)
PQ = PR = 7cm
hope you get your answer
Step-by-step explanation: