Home › Kerala SSLC (Class 10) › Mathematics › Tangents › Tangents at points A and B on a circle centred a…
Tangents at points A and B on a circle centred at O meet at an external point C. In the quadrilateral OACB, why is the quadrilateral cyclic?
AOpposite angles at A and B sum to 180 degrees as both are right angles
BThe diagonals bisect each other inside the quadrilateral
CAdjacent angles each measure exactly 90 degrees
DOpposite sides are equal in length
Answer & Solution
Correct answer: A. Opposite angles at A and B sum to 180 degrees as both are right angles
1. OA is a radius and CA is a tangent at A, so angle OAC = 90°.
2. Similarly OB is a radius and CB is a tangent at B, giving angle OBC = 90°.
3. The two opposite angles at A and B add to 90° + 90° = 180°.
4. A quadrilateral is cyclic if and only if a pair of opposite angles sum to 180°.
5. Hence OACB is cyclic by the opposite-angle criterion, not by side or diagonal properties.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 7 "Tangents" (pp 159-172, 2019 ed.)._
Related questions
In the chord-tangent picture, the angle which the chord makes with the tangent at one end Why does the construction of a tangent at a point P on a circle by drawing an arc centred To draw the tangent at a point on a circle without knowing the centre, one method uses anySides of a large triangle are tangent to the circumcircle of a small triangle, touching thA chord of a circle subtends a central angle of 60°. The angle between the tangent at one If the angle between a tangent and the chord at the point of contact is 30°, the inscribedIn a circle, the angle between two tangents drawn from an external point measures 70°. TheThe picture shows two tangents to a circle from an external point and the radii to the poi