Geometry Additional One Mark Online Test

Geometry Additional One Mark Online Test (10th Standard Mathematics)

Pick how many questions you want and set a time limit, then start. You'll get your score at the end with the correct answer and an explanation for every question. Free, in Tamil and English — 15 questions available.

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If the scale factor of two similar triangles is \(3 : 4\), what is the ratio of their corresponding areas?

A.\(3 : 4\) B.\(9 : 16\) C.\(16 : 9\) D.\(27 : 64\)

In \(\Delta ABC\), a line \(DE\) is drawn parallel to \(BC\) intersecting \(AB\) at \(D\) and \(AC\) at \(E\). If \(AD = 4\) cm, \(DB = 6\) cm, and \(AE = 6\) cm, what is the length of \(EC\)?

A.4 cm B.9 cm C.10 cm D.12 cm

In \(\Delta PQR\), \(PS\) is the internal bisector of \(\angle P\) meeting \(QR\) at \(S\). If \(PQ = 12\) cm, \(PR = 15\) cm, and \(QS = 4\) cm, find the length of \(SR\).

A.5 cm B.6 cm C.8 cm D.10 cm

A ladder of length 13 m is leaned against a vertical wall. If the foot of the ladder is 5 m away from the base of the wall, at what height does it reach the wall?

A.8 m B.12 m C.14 m D.15 m

A tangent \(PA\) is drawn from an external point \(P\) to a circle of radius 6 cm with centre \(O\). If the length of the tangent \(PA\) is 8 cm, find the distance \(OP\).

A.10 cm B.12 cm C.14 cm D.16 cm

If two tangents \(PA\) and \(PB\) are drawn to a circle with centre \(O\) from an external point \(P\) such that \(\angle APB = 80^{\circ}\), then what is the measure of \(\angle AOP\)?

A.\(40^{\circ}\) B.\(50^{\circ}\) C.\(60^{\circ}\) D.\(70^{\circ}\)

In \(\Delta ABC\), the cevians \(AD\), \(BE\), and \(CF\) are concurrent. If \(BD = 3\) cm, \(DC = 4\) cm, \(CE = 4\) cm, \(EA = 5\) cm, and \(AF = 10\) cm, what is the length of \(FB\)?

A.5 cm B.6 cm C.7.5 cm D.8 cm

A line cuts the sides \(BC\), \(CA\), and \(AB\) (or their extensions) of \(\Delta ABC\) at points \(D\), \(E\), and \(F\) respectively. If \(BD = 6\) cm, \(DC = 3\) cm, \(CE = 2\) cm, \(EA = 4\) cm, and \(AF = 3\) cm, find the length of \(FB\)?

A.1.5 cm B.3 cm C.4.5 cm D.6 cm

In a circle with centre \(O\), two tangents \(PA\) and \(PB\) are drawn from an external point \(P\). If the angle between the two tangents is \(110^{\circ}\), what is the measure of the central angle \(\angle AOB\)?

A.\(70^{\circ}\) B.\(80^{\circ}\) C.\(90^{\circ}\) D.\(110^{\circ}\)

Q10

In a circle, a chord \(AB\) makes an angle of \(65^{\circ}\) with the tangent \(BT\) at the point of contact \(B\). What is the angle \(\angle APB\) subtended by the chord in the major alternate segment?

A.\(65^{\circ}\) B.\(115^{\circ}\) C.\(130^{\circ}\) D.\(50^{\circ}\)

Q11

If the perimeters of two similar triangles \(\Delta ABC\) and \(\Delta PQR\) are 45 cm and 30 cm respectively, and \(AB = 15\) cm, what is the length of the corresponding side \(PQ\)?

A.10 cm B.12 cm C.8 cm D.15 cm

Q12

In \(\Delta ABC\), \(AB = 6\) cm, \(AC = 8\) cm, and \(AD\) is a line segment from \(A\) to \(BC\) such that \(BD = 3\) cm and \(DC = 4\) cm. Which of the following is true?

A.\(AD\) is parallel to \(BC\) B.\(AD\) is perpendicular to \(BC\) C.\(AD\) is the angle bisector of \(\angle BAC\) D.\(AD\) is the median of \(BC\)

Q13

How many tangents can be drawn to a circle from a point lying strictly inside the circle?

A.Zero B.One C.Two D.Infinitely many

Q14

If the sides of a right-angled triangle are \(x - 1\), \(x\), and \(x + 1\) (where \(x > 1\)), what is the value of \(x\)?

A.3 B.4 C.5 D.6

Q15

Two concentric circles have radii 13 cm and 5 cm. A chord of the larger circle is tangent to the smaller circle. Find the length of this chord.

A.12 cm B.18 cm C.24 cm D.26 cm

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About this Geometry test

This free online practice test covers Geometry from the 10th Standard Mathematics (Samacheer Kalvi) syllabus. Choose the number of questions and an optional time limit, then answer and submit — everything is checked in your browser, with the correct answers and a worked explanation shown at the end. For the full solutions to every question in this set, see the solved MCQs page.

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