In the figure , D is the centre of the circle and C is a point on the semi-circle with diameter DA. BC is a tangent through B.

If DB = 1 cm and AB = 3 cm, then $∠ C D B$ = _____

60^{\circ}

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50^{\circ}

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40^{\circ}

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70^{\circ}

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Solution

The correct option is A $60^{\circ}$
$D C^{2}$ = DB $\times$ DA

$D C^{2}$ = 1 $\times$ 4

DC = 2 cm

cos $∠ C D B$ = $\frac{D B}{D C}$ = $\frac{1}{2}$

$∴ ∠ C D B = 60^{\circ}$

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Similar questions

ABCD is a cyclic quadrilateral whose side AB is the diameter of the circle with centre O through A, B, C, D. If $∠ A D C = 130^{\circ}$ , Calculate $∠$ BAC.

Q. In the given figure, O is the centre of a circle. AOC is its diameter, such that ∠ACB = 50°. If AT is the tangent to the circle at the point A, then ∠BAT = ?

(a) 40°
(b) 50°
(c) 60°
(d) 65°

In the given figure, AB is a diameter and AC is a chord of the circle and the tangent at C intersects AB produced in D. If $∠ B A C = 30^{\circ}$ , then $∠ C D B =$ ______.

Q. In the given figure, O is the centre of a circle. If ∠OAB = 40°, then ∠ACB = ?
(a) 40°
(b) 50°
(c) 60°
(d) 70°

Q. Question 3
In figure, AB is a chord of the circle and AOC is its diameter such that

∠ A C B = 50^{\circ}

. If AT is the tangent to the circle at the point A, then

∠

BAT is equal to
(A) 65°
(B) 60°
(C) 50°
(D) 40°

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In the figure , D is the centre of the circle and C is a point on the semi-circle with diameter DA. BC is a tangent through B. If DB = 1 cm and AB = 3 cm, then ∠CDB = _____

The correct option is A 60∘DC2 = DB × DA DC2 = 1 × 4 DC = 2 cm cos∠CDB = DBDC = 12 ∴∠CDB=60∘

In the figure , D is the centre of the circle and C is a point on the semi-circle with diameter DA. BC is a tangent through B.

If DB = 1 cm and AB = 3 cm, then $∠ C D B$ = _____

The correct option is A $60^{\circ}$
$D C^{2}$ = DB $\times$ DA

$D C^{2}$ = 1 $\times$ 4

DC = 2 cm

cos $∠ C D B$ = $\frac{D B}{D C}$ = $\frac{1}{2}$

$∴ ∠ C D B = 60^{\circ}$