CBSE Class 10 Maths (Basic) 2023 · Paper 430/2/1 · Question 37

Circles 4 marks Hard

Circles play an important part in our life. When a circular object is hung on the wall with a cord at nail N, the cords NA and NB work like tangents. Observe the figure, given that

∠ A N O = 3 0^{\circ}

and

O A = 5

cm.

Circle hung at nail N with tangent cords NA, NB and chord AB.

(i)Find the distance AN.[1]
(ii)Find the measure of angle AOB.[1]
(iii)(a)Find the total length of cords NA, NB and the chord AB.[2]
(iii)(b)OR If angle ANO = 45 degrees, then name the type of quadrilateral OANB. Justify your answer.[2]

Answer

(i)

A N = 53 \approx 8.66

cm; (ii)

∠ A O B = 12 0^{\circ}

; (iii a)

N A + N B + A B = 153 \approx 25.98

cm; (iii b) OANB is a square when

∠ A N O = 4 5^{\circ}

🔒 Step-by-step solution

From the board paper

CBSE Class 10 Maths (Basic) 2023 · Paper 430/2/1, Question 37 — all 38 questions with answers →

CBSE Class 10 Maths (Basic) 2023 · Paper 430/2/1 · Question 37

Answer

From the board paper

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