Incircle and Its Construction
Trending Questions
In the given figure, △ABC is right-angled at B, in which AB = 15 cm and BC = 8 cm. A circle with center O has been inscribed in △ABC. Calculate the value of x, the radius of the inscribed circle. [4 MARKS]
Find the area of the segment of a circle of radius 12 cm whose corresponding sector has a central angle of 60∘. (use π=3.14)
In the given figure ΔABC is an isosceles traingle with AB=AC and ∠ABC = 50∘. Find ∠ BEC = \({x}^{0}\, find the value of x.
Find the value of x from the given figure, in which O is the centre of the circle.
Draw the incircle of equilateral triangle of side 5 cm. Measure the radius of the circle.
2 cm
3 cm
5 cm
1.4 cm
O is the centre of the circle. ∠OAB = 20∘, ∠OCB = 55∘. Then∠BOC= and \(\angle)AOC=
Congruent polygons have the same area.
False
True
Which of the following statements is/are correct?
1. The locus of the point of intersection of two perpendicular tangents is called director circle of the given circle.
2. The director circle of a circle is concentric circle.
3. The radius of director circle of a circle is equal to the radius of original circle.C
Only 1 & 2
Only 1
Only 1 & 3
All 1, 2 and 3
Prove that the quadrilateral formed by angle bisectors of a cyclic quadrilateral ABCD is also cyclic. [4 MARKS]
Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.
Construct a ΔPQRwith QR = 8 cm, PQ = 6 cm, PR = 4 cm. Construct the incircle of the triangle and find the radius of the incircle.
4 cm
2.2 cm
1.3 cm
5.4 cm
In the given figure, AB is the diameter of the circle. AC is equal to BC. Find the value of ∠ABC.
30°
45°
60°
90°
Column−IColumn−II(A) In the given figure, (p) 60∘ ABCD is a cyclic Quadrilateral. O is the centre of the circle. If ∠BOD=160∘ find the Measure of ∠BPD.
![](https://search-static.byjusweb.com/question-images/byjus/infinitestudent-images/ckeditor_assets/pictures/27385/content_110.png)
(B) In given figure, ABCD is a cyclic(q) 65∘ quadrilateral whose side AB is a diameter of the circle through A, B, C, D. If ∠ADC=130∘, find ∠BAC.
![](https://search-static.byjusweb.com/question-images/byjus/infinitestudent-images/ckeditor_assets/pictures/27386/content_111.png)
(C) In the given figure BD=DC and(r) 40∘ ∠CBD=30∘ Find m(∠BAC)
![](https://search-static.byjusweb.com/question-images/byjus/infinitestudent-images/ckeditor_assets/pictures/27388/content_112.png)
(D) In the given figure, O is the centre of the(s) 100∘ arc ABC subtends an angle of 130∘ at the centre. If AB is extended to Pm find ∠PBC.
![](https://search-static.byjusweb.com/question-images/byjus/infinitestudent-images/ckeditor_assets/pictures/27390/content_113.png)
Choose the correct option:
- A-s; B-r; C-p; D-q
- A-s; B-p; C-q; D-r
- A-p; B-q; C-r; D-s
- A-s; B-p; C-r; D-q
- circumradius
- inradius
- median
Show that the line segment joining the points of contact of two parallel tangents passes through the centre.
- 2cm
- 1cm
- 5cm
- 3cm
- Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
- Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
- Assertion is correct but Reason is incorrect
- Both Assertion and Reason are incorrect
[2 Marks]
- rhombus.
- square
- None of the above.
- rectangle
![1396192_d322837d986d4a96a2cead7cac7be088.jpg](https://search-static.byjusweb.com/question-images/toppr_ext/questions/1396192_d322837d986d4a96a2cead7cac7be088.jpg)
- 100
- 80
- 120
- 110
- Incentre
- Orthocentre
- Centroid
Use the following information to answer the next question.
How many diagonals containing point B or point D can be drawn in the given polygon?
12
7
9
10
![](https://search-static.byjusweb.com/question-images/byjus/_3ab972ffc4e4bc21f73102426d06bfaf5fb19b4320160912-20979-jos4f.png)
ABC, OD ⊥ BC, OE ⊥ AC and OF ⊥ AB. Then,
AF2+BD2+CE2=AE2+CD2+BF2
- True
- False
![103342.jpg](https://search-static.byjusweb.com/question-images/toppr_invalid/questions/103342.jpg)
- 10 cm
- 40 cm
- 50 cm
- 30 cm
- π4
- π6
- 3π4
- π3
![83573_a89605f1422e45759129a4ac80c0fc2a.png](https://search-static.byjusweb.com/question-images/toppr_ext/questions/83573_a89605f1422e45759129a4ac80c0fc2a.png)
- 62.5∘
- 125∘
- 55∘
- 45∘