Mathematics
Assertion (A): From a point P, 10 cm away from the centre of a circle, a tangent PT of length 8 cm is drawn, then the radius of the circle is 5 cm.
Reason (R): In a circle, radius through the point of contact is perpendicular to the tangent.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false
Answer
In a circle, radius through the point of contact is perpendicular to the tangent.
In right angled triangle OPT,
OP2 = OT2 + PT2
102 = OT2 + 82
OT2 = 100 - 64
OT2 = 36
OT = 6 cm.
Assertion (A) is false.
In a circle, the radius through the point of contact is perpendicular to the tangent is true.
Reason (R) is true.
A is false, R is true
Hence, option 2 is the correct option.
Related Questions
In the figure, XY is a tangent at X to the circle with centre O. If ∠XYO = 25°, then x = ?
25°
115°
65°
60°
In the given figure, XQY is a tangent at Q to a circle. If PM is a chord parallel to XY and ∠MQY = 70°, then ∠PQM = ?
20°
35°
40°
70°
Assertion (A): In the figure, AB, AC and DE are tangents to the circle. If AC = 7 cm, then perimeter of ΔADE is 14 cm.
Reason (R): The lengths of tangents to a circle from an exterior point are equal.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false
Assertion (A): In two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.
Reason (R): A line joining centre to any point of a chord of a circle bisects the chord.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false