Mathematics
In the given circle with centre O, PA and PB are tangents and ∠OAB = 28°, then ∠APB is :
90°
56°
62°
90° + 28°
Answer
We know that,
Tangent at any point of a circle and the radius through this point are perpendicular to each other.
∴ ∠OAP = 90°
From figure,
⇒ ∠PAB = ∠OAP - ∠OAB = 90° - 28° = 62°
PA and PB are tangents drawn to the circle from the external point P.
∴ PA = PB
We know that,
Angles opposite to equal sides of a triangle are equal.
∴ ∠PAB = ∠PBA = 62°
By angle sum property of triangle PAB,
⇒ ∠PAB + ∠PBA + ∠APB = 180°
⇒ 62° + 62° + ∠APB = 180°
⇒ ∠APB = 180° - 124° = 56°.
Hence, Option 2 is the correct option.
Related Questions
BC is a tangent to the circle with center O. OD is radius of the circle. If ∠DOC = 100°, ∠B is equal to :
50°
60°
40°
70°
PA and PB are tangents to a circle with center O. If angle BPA = 70°, the angle ACB is :
70°
105°
140°
55°
In the above figure, if ∠P = 50°, then reflex angle AOB is :
2 × 50°
180° - 60°
230°
none of these
In the given figure, O is the centre of the circle and AB is a tangent to the circle at B. If AB = 15 cm and AC = 7.5 cm, calculate the radius of the circle.
