Geometry One Mark Online Test — Class 10 Mathematics

Geometry One Mark Online Test (10th Standard Mathematics)

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If in triangles ABC and EDF, $\frac{AB}{DE} = \frac{BC}{FD}$ then they will be similar, when

A.$\angle B = \angle E$ B.$\angle A = \angle D$ C.$\angle B = \angle D$ D.$\angle A = \angle F$

In $\Delta LMN$, $\angle L = 60^{\circ}$, $\angle M = 50^{\circ}$. If $\Delta LMN \sim \Delta PQR$ then the value of $\angle R$ is

A.$40^{\circ}$ B.$70^{\circ}$ C.$30^{\circ}$ D.$110^{\circ}$

If $\Delta ABC$ is an isosceles triangle with $\angle C = 90^{\circ}$ and $AC = 5$ cm, then $AB$ is

A.2.5 cm B.5 cm C.10 cm D.$5\sqrt{2}$ cm

In a given figure $ST \parallel QR$, $PS = 2$ cm and $SQ = 3$ cm. Then the ratio of the area of $\Delta PQR$ to the area of $\Delta PST$ is

$ST \parallel QR, PS = 2 \text{ செ.மீ}, SQ = 3 \text{ செ.மீ} — Geometry, 10th Standard Mathematics$

A.25 : 4 B.25 : 7 C.25 : 11 D.25 : 13

The perimeters of two similar triangles $\Delta ABC$ and $\Delta PQR$ are 36 cm and 24 cm respectively. If $PQ = 10$ cm, then the length of $AB$ is

A.$6\frac{2}{3}$ cm B.$10\frac{2}{3}$ cm C.$66\frac{2}{3}$ cm D.15 cm

If in $\Delta ABC$, $DE \parallel BC$. $AB = 3.6$ cm, $AC = 2.4$ cm and $AD = 2.1$ cm then the length of $AE$ is

A.1.4 cm B.1.8 cm C.1.2 cm D.1.05 cm

In a $\Delta ABC$, $AD$ is the bisector of $\angle BAC$. If $AB = 8$ cm, $BD = 6$ cm and $DC = 3$ cm. The length of the side $AC$ is

A.6 cm B.4 cm C.3 cm D.8 cm

In the adjacent figure $\angle BAC = 90^{\circ}$ and $AD \perp BC$ then

$\angle BAC = 90^\circ, AD \perp BC — Geometry, 10th Standard Mathematics$

A.$BD \cdot CD = BC^2$ B.$AB \cdot AC = BC^2$ C.$BD \cdot CD = AD^2$ D.$AB \cdot AC = AD^2$

Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m, what is the distance between their tops?

A.13 m B.14 m C.15 m D.12.8 m

Q10

In the given figure, $PR = 26$ cm, $QR = 24$ cm, $\angle PAQ = 90^{\circ}$, $PA = 6$ cm and $QA = 8$ cm. Find $\angle PQR$

$PR = 26 \text{ செ.மீ}, QR = 24 \text{ செ.மீ}, \angle PAQ = 90^\circ, PA = 6 \text{ செ.மீ}, QA = 8 \text{ செ.மீ} — Geometry, 10th Standard Mathematics$

A.$80^{\circ}$ B.$85^{\circ}$ C.$75^{\circ}$ D.$90^{\circ}$

Q11

A tangent is perpendicular to the radius at the

A.centre B.point of contact C.infinity D.chord

Q12

How many tangents can be drawn to the circle from an exterior point?

A.one B.two C.infinite D.zero

Q13

The two tangents from an external point P to a circle with centre at O are PA and PB. If $\angle APB = 70^{\circ}$ then the value of $\angle AOB$ is

A.$100^{\circ}$ B.$110^{\circ}$ C.$120^{\circ}$ D.$130^{\circ}$

Q14

In figure CP and CQ are tangents to a circle with centre at O. ARB is another tangent touching the circle at R. If CP = 11 cm and BC = 7 cm, then the length of BR is

$CP = 11 \text{ செ.மீ}, BC = 7 \text{ செ.மீ} — Geometry, 10th Standard Mathematics$

A.6 cm B.5 cm C.8 cm D.4 cm

Q15

In figure if PR is tangent to the circle at P and O is the centre of the circle, then $\angle POQ$ is

PR என்பது வட்டத்தின் தொடுகோடு — Geometry, 10th Standard Mathematics

A.$120^{\circ}$ B.$100^{\circ}$ C.$110^{\circ}$ D.$90^{\circ}$

Q16

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.$27 : 64$

Q17

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

Q18

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

Q19

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

Q20

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

Q21

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.$70^{\circ}$

Q22

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

Q23

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

Q24

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.$110^{\circ}$

Q25

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.$50^{\circ}$

Q26

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

Q27

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 $BC$

Q28

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

Q29

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

Q30

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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