Home › Kerala SSLC (Class 10) › Mathematics › Tangents › All sides of a rhombus are tangents to a circle …
All sides of a rhombus are tangents to a circle inscribed in it. If one of the rhombus's interior angles measures 40°, which property must the diagonals of the rhombus retain in general?
AThe diagonals bisect each other at right angles
BThe diagonals each measure 4 cm regardless of side length
CThe diagonals are equal in length
DThe diagonals make 45° with each side of the rhombus
Answer & Solution
Correct answer: A. The diagonals bisect each other at right angles
1. The defining property of a rhombus is that all four sides are equal in length.
2. In any rhombus, the diagonals always bisect each other and meet at right angles.
3. This holds whether or not a circle is inscribed within it.
4. Equal diagonals would make it a square; a 40° interior angle excludes that case.
5. The 45° claim and the fixed-length claim do not follow from rhombus geometry.
_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