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Mathematics [2 Mark Question Answer]

Tangents and Intersecting Chords · ICSE STD 10 (ICSE - English Medium). 3 questions.

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[2 Mark Question Answer]

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Question 12 Marks
In the following figure, PQ is the tangent to the circle at A, DB is a diameter and O is the centre of the circle. If ∠ ADB = 30° and ∠ CBD = 60° ; calculate : ∠CDB
Answer
BD is the diameter.
∴ ∠ BCD = 90° (angle in a semi – circle)
Now in ΔBCD,
∠ CDB + ∠ CBD + ∠ BCD  =180°
⇒ ∠ CDB  + 60° + 90°  =180° 
⇒ ∠ CDB =180° - 150° = 30° 
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Question 22 Marks
In the following figure, PQ is the tangent to the circle at A, DB is a diameter and O is the centre of the circle. If ∠ ADB = 30° and ∠ CBD = 60° ; calculate ∠ PAD.
Answer
OA = OD (radii of the same circle)
∴ ∠ OAD  = ∠ ODA = 30°
But, OA ⊥ PQ
∴ ∠ PAD = ∠ OAP  - ∠ OAD = 90°  - 30° = 60°
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Question 32 Marks
In the given figure, diameter $AB$ and chord $CD$ of a circle meet at $P. PT$ is a tangent to the circle at $T. CD = 7.8 \ cm, PD = 5 \ cm, PB  = 4 \ cm.$ Find the length of tangent $PT.$
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Answer
Since $PT^2 = PC \times PD$
$\Rightarrow PT^2 = 12.8 \times 5$
$\Rightarrow PT^2 = 64$
$\Rightarrow PT^2 = 8 \ cm$
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[2 Mark Question Answer] - Mathematics STD 10 Questions - Vidyadip