NCERT Solutions for Class 9 Clat Chapter 10 Circles

Circles Here is the CBSE Clat Chapter 10 for Class 9 students. Summary and detailed explanation of the lesson, including the definitions of difficult words. All of the exercises and questions and answers from the lesson's back end have been completed. NCERT Solutions for Class 9 Clat Circles Chapter 10 NCERT Solutions for Class 9 Clat Circles Chapter 10 The following is a summary in Hindi and English for the academic year 2025-26. You can save these solutions to your computer or use the Class 9 Clat.

Question 1

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The angles of a quadrilateral are in the ratio 3:5:9: 13. Find all the angles of the quadrilateral.

Solution

Let ABCD be a quadrilateral in which
∠A : ∠B : ∠C : ∠D = 3 : 5 : 9 : 13
Sum of the ratios = 3 + 5 + 9+ 13 = 30
Also, ∠A + ∠B + ∠C + ∠D = 360°
Sum of all the angles of a quadrilateral is 360°
$therefore space space space space space space space space space space space space space space space space angle straight A equals 3 over 30 cross times 360 degree equals 36 degree space space space space space space space space space space space space space space space space space space space angle straight A equals 5 over 30 cross times 360 degree equals 60 degree space space space space space space space space space space space space space space space space space space space angle straight C equals 9 over 30 cross times 360 degree equals 108 degree and space space space space space space space space space space space space space space space angle straight D equals 13 over 30 cross times 360 degree equals 156 degree space space space space space space space space space space space space space space space space space space space$

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NCERT Solutions for Class 9 Clat Chapter 10 Circles

The angles of a quadrilateral are in the ratio 3:5:9: 13. Find all the angles of the quadrilateral.

If the diagonals of a parallelogram are equal, then show that it is a rectangle.

Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

Show that the diagonals of a square are equal and bisect each other at right angles.

Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.

Diagonal AC of a parallelogram ABCD bisects ∠A (see figure). Show that:
(i) it bisects ∠C also
(ii) ABCD is a rhombus.

ABCD is a rhombus. Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D.

ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. Show that (i) ABCD is a square (ii) diagonal BD bisects ∠B as well as ∠D.

In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see figure). Show that:

(i) ∆APD ≅ ∆CQB
(ii) AP = CQ
(iii) ∆AQB ≅ ∆CPD
(iv) AQ = CP
(v) APCQ is a parallelogram.

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD respectively (see figure). Show that:
(i) ∆APB ≅ ∆CQD
(ii) AP = CQ.

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NCERT Solutions for Class 9 Clat Chapter 10 Circles

The angles of a quadrilateral are in the ratio 3:5:9: 13. Find all the angles of the quadrilateral.

If the diagonals of a parallelogram are equal, then show that it is a rectangle.

Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

Show that the diagonals of a square are equal and bisect each other at right angles.

Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.

Diagonal AC of a parallelogram ABCD bisects ∠A (see figure). Show that:(i) it bisects ∠C also(ii) ABCD is a rhombus.

ABCD is a rhombus. Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D.

ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. Show that (i) ABCD is a square (ii) diagonal BD bisects ∠B as well as ∠D.

In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see figure). Show that: (i) ∆APD ≅ ∆CQB(ii) AP = CQ(iii) ∆AQB ≅ ∆CPD(iv) AQ = CP(v) APCQ is a parallelogram.

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD respectively (see figure). Show that:(i) ∆APB ≅ ∆CQD(ii) AP = CQ.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Diagonal AC of a parallelogram ABCD bisects ∠A (see figure). Show that:
(i) it bisects ∠C also
(ii) ABCD is a rhombus.

In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see figure). Show that:

(i) ∆APD ≅ ∆CQB
(ii) AP = CQ
(iii) ∆AQB ≅ ∆CPD
(iv) AQ = CP
(v) APCQ is a parallelogram.

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD respectively (see figure). Show that:
(i) ∆APB ≅ ∆CQD
(ii) AP = CQ.