RA and RB are two tangents from a common point lsquo R rsquo outside the circle with centre lsquo O ...........

Quantitative Aptitude (CHSL) Geometry

RA and RB are two tangents from a common point ‘R’ outside the circle with centre ‘O’, having a radius of 6 cm. If ∠ARB = 70°,

find the measure of the angle AOB.

This questions was previously asked in

SSC CHSL 25th May 2022 Shift-2

130^o

110^o

120^o

80^o

- When two tangents are drawn from an external point to a circle, they are equal in length. Therefore, ?ORA and ?ORB are isosceles triangles.

- The angles at the centres, ?OAR and ?OBR, are both right angles because tangents are perpendicular to the radius at the point of contact.

- In quadrilateral OARB, the sum of the angles is 360°.

- Using the property of tangents from an external point, ?OAR = ?OBR = 90°.

- So, ?AOB = 360° - ?ARB - ?OAR - ?OBR = 360° - 70° - 90° - 90° = 110°.

Therefore, Option 2: 110° is correct.

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