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प्रश्न
In the given figure, if chords AB and CD of the circle intersect each other at right angles, then x + y =
विकल्प
45°
60°
75°
90°
उत्तर
90°
We are given the following figure
∠ACD = ∠ABD (Angle in the same segment are equal)
⇒ ∠ACD = y
Consider the ΔACM in which
`angleACM + x + 90° = 180°`
` y + x + 90° = 180°`
`x + y = 90°`
APPEARS IN
संबंधित प्रश्न
In two concentric circles, prove that all chords of the outer circle which touch the inner circle are of equal length.
Write True or False. Give reason for your answer.
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AB and CD are two equal chords of a drde intersecting at Pas shown in fig. P is joined to O , the centre of the cirde. Prove that OP bisects ∠ CPB.
Draw a circle of radius 4.8 cm and mark its center as P.
(i) Draw radii PA and PB such that ∠APB = 45°.
(ii) Shade the major sector of the circle
If a chord AB subtends an angle of 60° at the centre of a circle, then angle between the tangents at A and B is also 60°.
If a hexagon ABCDEF circumscribe a circle, prove that AB + CD + EF = BC + DE + FA.
If A, B, C, D are four points such that ∠BAC = 30° and ∠BDC = 60°, then D is the centre of the circle through A, B and C.
AB is a chord of a circle with centre O. AOC is diameter of circle, AT is a tangent at A.
Write answers of the following questions:
- Draw the figure using the given information.
- Find the measures of ∠CAT and ∠ABC with reasons.
- Whether ∠CAT and ∠ABC are congruent? Justify your answer.
