10 Dec 2020 3:01 pm

**Tamilnadu, Samacheer, Kalvi, 10th, sslc, Maths, Solutions, Chapter 4, Algebra, Ex 4.5,**

Question 1.

If in triangles ABC and EDF, ABDE = BCFDthen they will be similar, when ……….

(1) ∠B = ∠E

(2) ∠A = ∠D

(3) ∠B = ∠D

(4) ∠A = ∠F

Answer:

(3) ∠B = ∠D

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°

Answer:

(2) 70°

Hint:

Since ∆LMN ~ ∆PQR

∠N = ∠R

∠N = 180 – (60 + 50)

= 180 – 110°

∠N = 70° ∴ ∠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 2–√ cm

Answer:

(4) 5 2–√ cm

Hint:

AB^{2} = AC^{2} + BC^{2}

AB^{2} = 5^{2} + 5^{2}

(It is an isosceles triangle)

AB = 50−−√ = 25×2−−−−−√

AB = 5 2–√

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

Answer:

(1) 25 : 4

Hint. Area of ∆PQR : Area of ∆PST

Area of ΔPQR Area of ΔPST=PQ2PS2=5222=254

Area of ∆PQR : Area of ∆PST = 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 ………….

(1) 6 23 cm

(2) 106√3

(3) 66 23 cm

(4) 15 cm

Answer:

(4) 15 cm

Hint:

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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

Answer:

(1) 1.4 cm

Hint:

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

Answer:

(2) 4 cm

Hint:

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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}

Answer:

(3) BD CD = AD^{2}

Hint:

Question 9.

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

(1) 13 m

(2) 14 m

(3) 15 m

(4) 12.8 m

Answer:

(1) 13 m

Hint:

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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°

Answer:

(4) 90°

Hint.

PR = 26 cm, QR = 24 cm, ∠PAQ = 90°

In the ∆PQR,

In the right ∆ APQ

PQ^{2} = PA^{2} + AQ^{2}

= 6^{2} + 8^{2}

= 36 + 64 = 100

PQ = 100−−−√ = 10

∆ PQR is a right angled triangle at Q. Since

PR^{2} = PQ^{2} + QR^{2}

∠PQR = 90°

Question 11.

A tangent is perpendicular to the radius at the

(1) centre

(2) point of contact

(3) infinity

(4) chord

Solution:

(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

Answer:

(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°

Answer:

(2) 110°

Hint.

∠OAP = 90°

∠APO = 35°

∠AOP = 180 – (90 + 35)

= 180 – 125 = 55

∠AOB = 2 × 55 = 110°

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Question 14.

In figure CP and CQ are tangents to a circle with centre at 0. 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

Answer:

(4) 4 cm

Hint.

BQ = BR = 4 cm (tangent of the circle)

PC = QC = 11 cm (tangent of the circle)

QC = 11 cm

QB + BC = 11

QB + 7 = 11

QB = 11 – 7 = 4 cm

BR = BQ = 4 cm

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°

Answer:

(1) 120°

Hint.

Since PR is tangent of the circle.

∠QPR = 90°

∠OPQ = 90° – 60° = 30°

∠OQB = 30°

In ∆OPQ

∠P + ∠Q + ∠O = 180°

30 + 30° + ∠O = 180°

(OP and OQ are equal radius)

∠O = 180° – 60° = 120°