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- Circles : Solution of NCERT Exercise 10.2 - part - 4

Exercise 10.2

Question: 8 - A quadrilateral ABCD is drawn to circumscribe a circle. Prove that: AB + CD = AD + BC

Answer: Construction: Draw a circle with centre O. Draw a quadrilateral ABCD which touches the circle at P, Q, R and S.

To Prove: AB + CD = AD + BC

AP = AS

BP = BQ

CQ = CR

DR = DS

(Tangents from same external point are equal)

Adding all the four equations from above; we get:

AP + BP + CR + DR = AS + DS + BQ + CQ

Or, (AP + BP) + (CR + DR) = (AS + DS) + (BQ + CQ)

Or, AB + CD = AD + BC proved

Question: 9 - In the given figure, XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X'Y' at B. Prove that ïƒAOB = 90Â°

Answer:

In Î”APO and Î”ACO

AP = AC (tangents from a point)

OP = OC (radii)

OA = OA (common side)

Hence; Î”APO â‰ˆ Î”ACO

So, ∠PAO = ∠CAO

Hence; AO is the bisector of ∠PAC.

Similarly, it can be proved that

BO is the bisector of ∠QBC

Now, XY || X'Y' (given)

So, ∠AOB = Right angle

(Bisectors of internal angles on one side of transversal intersect at right angle.

- 10th Maths Paper Solutions Set 2 : CBSE Delhi Previous Year 2015
- 10th Maths Paper Solutions Set 3 : CBSE Delhi Previous Year 2015
- 10th Maths Paper Solutions Set 1 : CBSE Delhi Previous Year 2015
- 10th Maths Paper Solutions Set 1 : CBSE Abroad Previous Year 2015
- 10th Maths Paper Solutions Set 1 : CBSE All India Previous Year 2015

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Introduction
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NCERT Solution - Exercise 3.1
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NCERT Solution - Exercise 3.2 Part-1
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NCERT Solution - Exercise 3.2 Part-2
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NCERT Solution - Exercise 3.3 Part-1
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NCERT Solution - Exercise 3.3 Part-2
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NCERT Solution - Exercise 3.4 Part-1
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NCERT Solution - Exercise 3.4 Part-2
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NCERT Solution - Exercise 3.5 Part-1
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NCERT Solution - Exercise 3.5 Part-2
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NCERT Solution - Exercise 3.6 Part-1
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NCERT Solution - Exercise 3.6 Part-2
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NCERT Solution - Exercise 4.1 Part-1
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NCERT Solution - Exercise 4.1 Part-2
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NCERT Solution - Exercise 4.2 Part-1
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NCERT Solution - Exercise 4.2 Part-2
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NCERT Solution - Exercise 4.2 Part-3
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NCERT Solution - Exercise 4.3 Part-1
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NCERT Solution - Exercise 4.3 Part-2
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NCERT Solution - Exercise 4.3 Part-3
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NCERT Solution - Exercise 4.3 Part-4
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NCERT Solution - Exercise 4.3 Part-5
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NCERT Solution - Exercise 4.4 Part-1
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NCERT Solution - Exercise 4.4 Part-2
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Solution of Exercise 5.1 (NCERT)-Part-1
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Solution of Exercise 5.1 (NCERT)-Part-2
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Solution of Exercise 5.1 (NCERT)-Part-3.1
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Solution of Exercise 5.1 (NCERT)-Part-3.2
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Solution of Exercise 5.2 (NCERT) Part -1
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Solution of Exercise 5.2 (NCERT) Part -2
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Solution of Exercise 5.2 (NCERT) Part -3
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Solution of Exercise 5.2 (NCERT) Part -4
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Solution of Exercise 5.2 (NCERT) Part -5
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Solution of Exercise 5.2 (NCERT) Part -6
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Solution of Exercise 5.3 (NCERT)Part -1
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Solution of Exercise 5.3 (NCERT)Part - 2
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Solution of Exercise 5.3 (NCERT)Part - 3
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Solution of Exercise 5.3 (NCERT)Part - 4
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Solution of Exercise 5.3 (NCERT)Part - 5
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Solution of Exercise 5.3 (NCERT)Part - 6
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Solution of Exercise 5.3 (NCERT)Part - 7
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Solution of Exercise 5.3 (NCERT)Part - 8
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Solution of NCERT Exercise 5.4 (Optional)
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Introduction : Theorems
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NCERT Solution of Exercise 6.1
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NCERT Solution Exercise 6.2 Part - I
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NCERT Solution Exercise 6.2 Part - II
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NCERT Solution Exercise 6.2 Part - III
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NCERT Solution of Exercise 6.3 Part - III
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NCERT Solution of Exercise 6.4
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NCERT Solution of Exercise 6.5
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NCERT Solution of Exercise 6.5 Part - 2
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NCERT Solution of Exercise 6.6 - Part - 1
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NCERT Solution of Exercise 6.6 - Part - 2
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THEOREM 1:
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Solution of NCERT Exercise 10.1
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Solution of NCERT Exercise 10.2
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Solution of NCERT Exercise 10.2 - Part 2
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Solution of NCERT Exercise 10.2 - part - 3
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Solution of NCERT Exercise 10.2 - part - 4
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Solution of NCERT Exercise 10.2 - part - 5
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Solution of NCERT Exercise 10.2 - part - 6
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