Math, asked by purvi1717, 3 months ago

All practice sets solution of Circle lesson 10th std . Maths part 2.
please Please please :(

Answers

Answered by devindersaroha43

Answer:

Step-by-step explanation:

Two circles having radii 3.5 cm and 4.8 cm touch each other internally. Find the distance between their centres.

Solution:

Let the two circles having centres P and Q touch each other internally at point R.

Here, QR = 3.5 cm, PR = 4.8 cm

Maharashtra Board Class 10 Maths Solutions Chapter 3 Circle Practice Set 3.2 1

The two circles touch each other internally.

∴ By theorem of touching circles,

P – Q – R

PQ = PR – QR

= 4.8 – 3.5

= 1.3 cm

[The distance between the centres of circles touching internally is equal to the difference in their radii]

Question 2.

Two circles of radii 5.5 cm and 4.2 cm touch each other externally. Find the distance between their centres.

Solution:

Let the two circles having centres P and R touch each other externally at point Q.

Here, PQ = 5.5 cm, QR = 4.2 cm

Maharashtra Board Class 10 Maths Solutions Chapter 3 Circle Practice Set 3.2 2

The two circles touch each other externally.

∴ By theorem of touching circles,

P – Q – R

PR = PQ + QR

= 5.5 + 4.2

= 9.7 cm

[The distance between the centres of the circles touching externally is equal to the sum of their radii]

Question 3.

If radii of two circles are 4 cm and 2.8 cm. Draw figure of these circles touching each other

i. externally

ii. internally.

Solution:

i. Circles touching externally:

Maharashtra Board Class 10 Maths Solutions Chapter 3 Circle Practice Set 3.2 3

ii. Circles touching internally:

Maharashtra Board Class 10 Maths Solutions Chapter 3 Circle Practice Set 3.2 4

Question 4.

In the adjoining figure, the circles with centres P and Q touch each other at R A line passing through R meets the circles at A and B respectively. Prove that –

Maharashtra Board Class 10 Maths Solutions Chapter 3 Circle Practice Set 3.2 5

i. seg AP || seg BQ,

ii. ∆APR ~ ∆RQB, and

iii. Find ∠RQB if ∠PAR = 35°.

Solution:

The circles with centres P and Q touch each other at R.

∴ By theorem of touching circles,

P – R – Q

i. In ∆PAR,

seg PA = seg PR [Radii of the same circle]

∴ ∠PRA ≅ ∠PAR (i) [Isosceles triangle theorem]

Similarly, in ∆QBR,

seg QR = seg QB [Radii of the same circle]

∴ ∠RBQ ≅ ∠QRB (ii) [Isosceles triangle theorem]

But, ∠PRA ≅ ∠QRB (iii) [Vertically opposite angles]

∴ ∠PAR ≅ ∠RBQ (iv) [From (i) and (ii)]

But, they are a pair of alternate angles formed by transversal AB on seg AP and seg BQ.

∴ seg AP || seg BQ [Alternate angles test]

ii. In ∆APR and ∆RQB,

∠PAR ≅ ∠QRB [From (i) and (iii)]

∠APR ≅ ∠RQB [Alternate angles]

∴ ∆APR – ∆RQB [AA test of similarity]

iii. ∠PAR = 35° [Given]

∴ ∠RBQ = ∠PAR= 35° [From (iv)]

In ∆RQB,

∠RQB + ∠RBQ + ∠QRB = 180° [Sum of the measures of angles of a triangle is 180°]

∴ ∠RQB + ∠RBQ + ∠RBQ = 180° [From (ii)]

∴ ∠RQB + 2 ∠RBQ = 180°

∴ ∠RQB + 2 × 35° = 180°

∴ ∠RQB + 70° = 180°

∴ ∠RQB = 110°

Question 5.

In the adjoining figure, the circles with centres A and B touch each other at E. Line l is a common tangent which touches the circles at C and D respectively. Find the length of seg CD if the radii of the circles are 4 cm, 6 cm.

Maharashtra Board Class 10 Maths Solutions Chapter 3 Circle Practice Set 3.2 6

Construction : Draw seg AF ⊥ seg BD.

Solution:

i. The circles with centres A and B touch each other at E. [Given]

∴ By theorem of touching circles,

A – E – B

Maharashtra Board Class 10 Maths Solutions Chapter 3 Circle Practice Set 3.2 7

∴ ∠ACD = ∠BDC = 90° [Tangent theorem]

∠AFD = 90° [Construction]

∴ ∠CAF = 90° [Remaining angle of ꠸AFDC]

∴ ꠸AFDC is a rectangle. [Each angle is of measure 900]

∴ AC = DF = 4 cm [Opposite sides of a rectangle]