Mathematics
The angle between two radii of a circle is 60°. The angle between their corresponding tangents is :
60°
90°
120°
150°
Answer
From figure,
∠OAP = ∠OBP = 90° [The radius and tangent of a circle at a point of contact is always perpendicular to each other.]
In quadrilateral OABP,
By angle sum property of quadrilateral,
⇒ ∠OAP + ∠OBP + ∠AOB + ∠APB = 360°
⇒ 90° + 90° + 60° + ∠APB = 360°
⇒ 240° + ∠APB = 360°
⇒ ∠APB = 360° - 240° = 120°.
Hence, Option 3 is the correct option.
Related Questions
O is center of the the circle and ∠AOB = 60°. The length of chord AB is :
equal to radius of the circle
equal to the side of a regular pentagon
bigger than the radius of the circle
smaller than the radius of the circle.
A regular eight-sided polygon ABCDEF is drawn about a circle with center O, the angle DOE is :
60°
80°
45°
90°
ABC is an isosceles triangle with AB = AC. Circles are drawn with AB and AC as diameters. The two circles intersect each other at vertex A and a point P which lies in side BC, ∠APB is :
60°
75°
90°
120°
ABC is a triangle. In order to draw a tangent PQ to the circle at point A, the angle BAQ is drawn equal to :
∠BAC
∠BCA
∠ABC
∠PAC