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## Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 4 Geometry Ex 4.5

Multiple choice questions.

Question 1.

If in triangles ABC and EDF, \(\frac{\mathbf{A B}}{\mathbf{D E}}=\frac{\mathbf{B C}}{\mathbf{F D}}\) then they will be similar, when

(1) ∠B = ∠E

(2) ∠A = ∠D

(3) ∠B = ∠D

(4) ∠A = ∠F

Solution:

(1) ∠B = ∠E

Hint:

Question 2.

In, ∆LMN, ∠L = 60°, ∠M =50° . If ∆LMN ~ ∆PQR then the value of ∠R is

(1) 40°

(2) 70°

(3) 30°

(4) 110°

Solution:

(2) 70°

∆LMN ~ ∆PQR, ∠R = 70°.

Question 3.

If ∆ABC is an isosceles triangle with ∠C = 90° and AC = 5 cm, then AB is

(1) 2.5 cm

(2) 5 cm

(3) 10 cm

(4) \(5 \sqrt{2}\) cm

Solution:

(4) \(5 \sqrt{2}\)cm

Hint:

Question 4.

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

(1) 25 : 4

(2) 25 : 7

(3) 25 : 11

(4) 25 : 13

Solution:

(1) 25 : 4

Hint:

Ratio of the area of similar triangles is equal to the ratio of the square of their corresponding sides.

∴ 5^{2} : 2^{2} = 25 : 4

Question 5.

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

Solution:

(4) 15 cm

Hint:

Question 6.

If in ∆ABC, DE || BC . AB = 3.6 cm, AC = 2.4 cm and AD = 2.1 cm then the length of AE is

(1) 1.4 cm

(2) 1.8 cm

(3) 1.2 cm

(4) 1.05 cm

Solution:

(1) 1.4 cm

\(\frac{3 \cdot 6}{2 \cdot 1}=\frac{2 \cdot 4}{\mathrm{A} \cdot \mathrm{E}}\)

(3.6) (AE) = 2.1 × 2.4

AE = 1.4 cm

Question 7.

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

(1) 6 cm

(2) 4 cm

(3) 3 cm

(4) 8 cm

Solution:

(2) 4 cm

Hint:

Question 8.

In the adjacent figure ∠BAC = 90° and AD ⊥ BC then

(1) BD.CD = BC^{2}

(2) AB.AC = BC^{2}

(3) BD.CD = AD^{2}

(4) AB.AC = AD^{2}

Solution:

(3) BD.CD = AD^{2}

Question 9.

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?

(1) 13 cm

(2) 14 m

(3.) 15 m

(4) 12.8 m

Solution:

(1) 13 cm

Hint:

Question 10.

In the given figure, PR = 26 cm, QR = 24 cm, PAQ = 90° , PA = 6 cm and QA = 8 cm. Find ∠PQR

(1) 80°

(2) 85°

(3) 75°

(4) 90°

Solution:

(4) 90°

Hint:

PR = 26

QR = 24

∠PAQ = 90°

PQ = 10

PQ = \(\sqrt{26^{2}-24^{2}}=\sqrt{100}\) = 10

∴ ∠PAQ = 90°

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 P to a circle with centre at O are PA and PB. If ∠APB = 70° then the value of ∠AOB is

(1) 100°

(2) 110°

(3) 120°

(4) 130°

Solution:

(2) 110°

Hint:

Question 14.

In figure CP and CQ are tangents to a circle T 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

(1) 6 cm

(2) 5 cm

(3) 8 cm

(4) 4 cm

Solution:

(4) 4 cm

BQ = BR

CP = CQ = 11

BC = 7, ∴ BQ = CQ – BC

= 11 – 7 = 4

BR = BQ = 4cm

Question 15.

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

(1) 120°

(2) 100°

(3) 110°

(4) 90°

Solution:

(1) 120°

∠POQ = 180° -(30° + 30°)

= 180° – 60°

= 120°