Class 10 Mathematics – Geometry (Unit 3) Quiz

In the given diagram, \(\triangle ABC \sim \triangle PQR\). If \(AD\) and \(PS\) are the bisectors of \(\angle BAC\) and \(\angle QPR\) respectively, then:

The areas of two similar triangles are in the ratio \(4 : 9\). The ratio of their corresponding sides is:

In \(\triangle ABC\), \(DE \parallel BC\) with \(AD = 2.5\text{ cm}\), \(DB = 5\text{ cm}\) and \(AE = 3\text{ cm}\). Then \(EC\) equals:

In \(\triangle ABC\), \(DE \parallel BC\). If \(AD = 4\text{ cm}\), \(DB = 6\text{ cm}\) and \(AE = 5\text{ cm}\), then \(EC\) is:

\(\triangle ABC \sim \triangle DEF\) with \(AB = 6\text{ cm}\) and \(DE = 4\text{ cm}\). If the area of \(\triangle DEF\) is \(20\text{ cm}^2\), the area of \(\triangle ABC\) is:

A vertical pole \(6\text{ m}\) high casts a shadow \(4\text{ m}\) long. At the same time, a tower casts a shadow \(20\text{ m}\) long. The height of the tower is:

The locus of a point equidistant from two given points \(A\) and \(B\) is:

The locus of a point at a fixed distance of \(3\text{ cm}\) from a fixed point \(O\) is:

The locus of a point equidistant from two intersecting straight lines is:

The locus of the centre of a circle of radius \(2\text{ cm}\) which touches a given line \(l\) is:

The locus of a point that is equidistant from the two arms of a given angle is:

The locus of a point equidistant from two given parallel lines is:

In a circle with centre \(O\), the angle subtended by a chord \(AB\) at the centre is \(110^\circ\). The angle subtended by \(AB\) at a point on the major arc is:

\(ABCD\) is a cyclic quadrilateral with \(\angle A = 68^\circ\). Then \(\angle C\) equals:

\(AB\) is a diameter of a circle and \(C\) is a point on the circle with \(\angle ABC = 35^\circ\). Then \(\angle BAC\) equals:

In a circle with centre \(O\), chord \(AB\) subtends \(\angle AOB = 80^\circ\) at the centre. The angle subtended by \(AB\) at a point \(C\) on the major arc is:

A chord of length \(24\text{ cm}\) is drawn in a circle of radius \(13\text{ cm}\). The perpendicular distance of the chord from the centre is:

In a cyclic quadrilateral \(ABCD\), \(\angle B = 110^\circ\). Then \(\angle D\) equals:

In the given diagram, \(PS\) and \(PT\) are tangents to the circle. \(SQ \parallel PT\) and \(\angle SPT = 80^\circ\). The value of \(\angle QST\) is:

In the given diagram, \(RT\) is a tangent touching the circle at \(S\). If \(\angle PST = 30^\circ\) and \(\angle SPQ = 60^\circ\), then \(\angle PSQ\) equals:

A tangent at a point on a circle makes an angle of \(30^\circ\) with a chord through the point of contact. The angle made by the chord in the alternate segment is:

From an external point \(P\), a tangent \(PT\) of length \(12\text{ cm}\) is drawn, and a secant \(PAB\) cuts the circle with \(PA = 8\text{ cm}\). The length of \(PB\) is:

Two chords \(AB\) and \(CD\) of a circle intersect at a point \(P\) inside the circle. If \(PA = 6\text{ cm}\), \(PB = 8\text{ cm}\) and \(PC = 4\text{ cm}\), then \(PD\) equals:

Two chords \(AB\) and \(CD\) of a circle intersect at a point \(P\) inside the circle. If \(PA = 4\text{ cm}\), \(PB = 12\text{ cm}\) and \(PC = 6\text{ cm}\), then \(PD\) equals:

The circumcentre of a triangle is the point which is:

To construct the circumcircle of a triangle, you draw the:

To construct the incircle of a triangle, you draw the:

To locate a point that is equidistant from two fixed points \(A\) and \(B\) during a construction, you draw the:

To construct a triangle given its base \(BC\), the base angle \(\angle B\) and the sum \(AB + AC\), the first step is to:

The point of intersection of the perpendicular bisectors of the sides of a triangle is the: