Advertisements
Advertisements
Question
In the given figure, if chords AB and CD of the circle intersect each other at right angles, then x + y =
Options
45°
60°
75°
90°
Advertisements
Solution
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
RELATED QUESTIONS
In the given figure, a circle inscribed in a triangle ABC, touches the sides AB, BC and AC at points D, E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10 cm, find the lengths of AD, BE and CF.
In the given figure, a circle touches all the four sides of a quadrilateral ABCD whose three sides are AB = 6 cm, BC = 7 cm and CD = 4 cm. Find AD.
Prove that the line segment joining the points of contact of two parallel tangents of a circle, passes through its centre.
In two concentric circles, a chord of length 8 cm of the large circle touches the smaller circle. If the radius of the larger circle is 5 cm, then find the radius of the smaller circle.
In Fig., chords AB and CD of the circle intersect at O. AO = 5 cm, BO = 3 cm and CO = 2.5 cm. Determine the length of DO.
Draw a line AB = 8.4 cm. Now draw a circle with AB as diameter. Mark a point C on the circumference of the circle. Measure angle ACB.
The diameter of a circle is 12.6 cm. State, the length of its radius.
Draw a circle of diameter 7 cm. Draw two radii of this circle such that the angle between these radii is 90°. Shade the minor sector obtained. Write a special name for this sector.
In the figure, a circle touches all the sides of quadrilateral ABCD from the inside. The center of the circle is O. If AD⊥ DC and BC = 38, QB = 27, DC = 25, then find the radius of the circle.
In the following figure, O is the centre of the circle. Name all radii of the circle.
