Exercise 4.5 - Chapter 4 Geometry 10th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

$\mathbf{E x} 4.5$
Multiple choice questions.
Question 1.
If in triangles $\mathrm{ABC}$ and $\mathrm{EDF}, \frac{\mathrm{AB}}{\overline{\mathrm{DE}}}=\frac{\mathrm{BC}}{\overline{F D}}$ then they will be similar, when
(1) $\angle B=\angle E$
(2) $\angle A=\angle D$
(3) $\angle \mathrm{B}=\angle \mathrm{D}$
(4) $\angle \mathrm{A}=\angle \mathrm{F}$
Solution:
(1) $\angle B=\angle E$

Question $2 .$
In, $\triangle \mathrm{LMN}, \angle \mathrm{L}=60^{\circ}, \angle \mathrm{M}=50^{\circ}$. If $\triangle \mathrm{LMN} \sim \triangle \mathrm{PQR}$ then the value of $\angle \mathrm{R}$ is
(1) $40^{\circ}$
(2) $70^{\circ}$
(3) $30^{\circ}$
(4) $110^{\circ}$
Solution:
(2) $70^{\circ}$

Question $3 .$
If $\triangle \mathrm{ABC}$ is an isosceles triangle with $\angle \mathrm{C}=90^{\circ}$ and $\mathrm{AC}=5 \mathrm{~cm}$, then $\mathrm{AB}$ is
(1) $2.5 \mathrm{~cm}$
(2) $5 \mathrm{~cm}$
(3) $10 \mathrm{~cm}$
(4) $5 \sqrt{2} \mathrm{~cm}$
Solution:
(4) $5 \sqrt{2} \mathrm{~cm}$

Question $4 .$
In a given figure $S T \| Q R, P S=2 \mathrm{~cm}$ and $S Q=3 \mathrm{~cm}$. Then the ratio of the area of $\triangle \mathrm{PQR}$ to the area of $\triangle \mathrm{PST}$ is

(1) $25: 4$
(2) $25: 7$
(3) $25: 11$
(4) $25: 13$
Solution:
(1) $25: 4$

Question $5 .$
The perimeters of two similar triangles $\triangle \mathrm{ABC}$ and $\triangle \mathrm{PQR}$ are $36 \mathrm{~cm}$ and $24 \mathrm{~cm}$ respectively. If $\mathrm{PQ}$ $=10 \mathrm{~cm}$, then the length of $\mathrm{AB}$ is
(1) $6 \frac{2}{3} \mathrm{~cm}$
(2) $\frac{10 \sqrt{6}}{3} \mathrm{~cm}$
(3) $66 \frac{2}{3} \mathrm{~cm}$
(4) $15 \mathrm{~cm}$
Solution:
(4) $15 \mathrm{~cm}$

Question $6 .$
If in $\triangle \mathrm{ABC}, \mathrm{DE} \| \mathrm{BC} \cdot \mathrm{AB}=3.6 \mathrm{~cm}, \mathrm{AC}=2.4 \mathrm{~cm}$ and $\mathrm{AD}=2.1 \mathrm{~cm}$ then the length of $\mathrm{AE}$ is
(1) $1.4 \mathrm{~cm}$
(2) $1.8 \mathrm{~cm}$
(3) $1.2 \mathrm{~cm}$
(4) $1.05 \mathrm{~cm}$
Solution:
(1) $1.4 \mathrm{~cm}$

Question $7 .$
In a $\triangle \mathrm{ABC}, \mathrm{AD}$ is the bisector of $\angle \mathrm{BAC}$. If $\mathrm{AB}=8 \mathrm{~cm}, \mathrm{BD}=6 \mathrm{~cm}$ and $\mathrm{DC}=3 \mathrm{~cm}$. The length of the side $\mathrm{AC}$ is
(1) $6 \mathrm{~cm}$
(2) $4 \mathrm{~cm}$
(3) $3 \mathrm{~cm}$
(4) $8 \mathrm{~cm}$
Solution:
(2) $4 \mathrm{~cm}$

Question $8 .$
In the adjacent figure $\angle \mathrm{BAC}=90^{\circ}$ and $\mathrm{AD} \perp \mathrm{BC}$ then

(1) $\mathrm{BD} \cdot \mathrm{CD}=\mathrm{BC}^{2}$
(2) $\mathrm{AB} \cdot \mathrm{AC}=\mathrm{BC}^{2}$
(3) $\mathrm{BD} \cdot \mathrm{CD}=\mathrm{AD}^{2}$
(4) $\mathrm{AB} \cdot \mathrm{AC}=\mathrm{AD}^{2}$
Solution:
(3) $\mathrm{BD} \cdot \mathrm{CD}=\mathrm{AD}^{2}$

Question 9 ,
Two poles of heights $6 \mathrm{~m}$ and $11 \mathrm{~m}$ stand vertically on a plane ground. If the distance between their feet is $12 \mathrm{~m}$, what is the distance between their tops?
(1) $13 \mathrm{~cm}$
(2) $14 \mathrm{~m}$
(3.) $15 \mathrm{~m}$
(4) $12.8 \mathrm{~m}$
Solution:
(1) $13 \mathrm{~cm}$

Question $10 .$
In the given figure, $\mathrm{PR}=26 \mathrm{~cm}, \mathrm{QR}=24 \mathrm{~cm}, \mathrm{PAQ}=90^{\circ}, \mathrm{PA}=6 \mathrm{~cm}$ and $\mathrm{QA}=8 \mathrm{~cm}$. Find $\angle \mathrm{PQR}$
(1) $80^{\circ}$
(2) $85^{\circ}$
(3) $75^{\circ}$
(4) $90^{\circ}$
Solution:
(4) $90^{\circ}$

Question 11.
A tangent is perpendicular to the radius at the
(1) centre
(2) point of contact
(3) infinity
(4) chord
Answer:
(2) point of contact

Question $12 .$
How many tangents can be drawn to the circle from an exterior point?
(1) one
(2) two
(3) infinite
(4) zero
Solution:
(2) two

Question $13 .$
The two tangents from an external points $\mathrm{P}$ to a circle with centre at $\mathrm{O}$ are $\mathrm{PA}$ and $\mathrm{PB}$. If $\angle \mathrm{APB}=$ $70^{\circ}$ then the value of $\angle \mathrm{AOB}$ is
(1) $100^{\circ}$
(2) $110^{\circ}$
(3) $120^{\circ}$
(4) $130^{\circ}$
Solution:
(2) $110^{\circ}$

Question $14 .$
In figure $\mathrm{CP}$ and $\mathrm{CQ}$ are tangents to a circle $\mathrm{T}$ with centre at $\mathrm{O}$. $\mathrm{ARB}$ is another tangent touching the circle at $R$. If $C P=11 \mathrm{~cm}$ and $B C=7 \mathrm{~cm}$, then the length of $B R$ is
(1) $6 \mathrm{~cm}$
(2) $5 \mathrm{~cm}$
(3) $8 \mathrm{~cm}$
(4) $4 \mathrm{~cm}$
Solution:
(4) $4 \mathrm{~cm}$

Question $15 .$
In figure if $P R$ is tangent to the circle at $P$ and $O$ is the centre of the circle, then $\angle P O Q$ is
(1) $120^{\circ}$
(2) $100^{\circ}$
(3) $110^{\circ}$
(4) $90^{\circ}$
Solution:
(1) $120^{\circ}$