from a point C, the length of the the tangent to a circle is 8cm and the distance of Q from the centre is 10cm the radius of the circle is perpendicular to the radius though the point of the circle is 36 cm
Answers
Answer:
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Step-by-step explanation:
Given:- A circle with center O and AB is the tangent from point A.
Radius of circle =OB=8cm
Distance of point from the circle =AO=10cm
To find:- Length of tangent, i.e., AB=?
Solution:-
Since AB is tangent,
Therefore,
AB⊥OB[∵Tangent at any point of circle is perpendicular to the radius through point of contact]
⇒∠ABO=90°
Hence △OAB is a right angle triangle.
Using pythagoras theorem in △OAB,
AO
2
=AB
2
+OB
2
(10)
2
=AB
2
+(8)
2
⇒AB=
100−64
=6cm
Hence the length of tangent is 6cm.
Hence the correct answer is 6cm.
Answer:
Given:- A circle with center O and AB is the tangent from point A.
Radius of circle =OB=8cm
Distance of point from the circle =AO=10cm
To find:- Length of tangent, i.e., AB=?
Solution:-
Since AB is tangent,
Therefore,
AB⊥OB[∵Tangent at any point of circle is perpendicular to the radius through point of contact]
⇒∠ABO=90°
Hence △OAB is a right angle triangle.
Using pythagoras theorem in △OAB,
AO
2
=AB
2
+OB
2
(10)
2
=AB
2
+(8)
2
⇒AB=
100−64
=6cm
Hence the length of tangent is 6cm.
Hence the correct answer is 6cm.