Advertisements
Advertisements
प्रश्न
Four alternative answers for the following question is given. Choose the correct alternative.
Seg XZ is a diameter of a circle. Point Y lies in its interior. How many of the following statements are true ? (i) It is not possible that ∠XYZ is an acute angle. (ii) ∠XYZ can’t be a right angle. (iii) ∠XYZ is an obtuse angle. (iv) Can’t make a definite statement for measure of ∠XYZ.
विकल्प
Only one
Only two
Only three
All
उत्तर
Let P be any point on the arc XZ. 
XZ is the diameter of the circle.
∴ ∠XPZ = 90º (Angle in a semi-circle is 90º)
So, ∠XYZ cannot be a right angle.
In ∆YPZ,
∠XYZ > ∠YPZ (An exterior angle of a triangle is greater than its remote interior angle)
⇒ ∠XYZ > 90º (∠YPZ = ∠XPZ)
So, ∠XYZ is an obtuse angle. Therefore, it is not possible that ∠XYZ is an acute angle.
Thus, three of the following statements are true.
Hence, the correct answer is Only three .
APPEARS IN
संबंधित प्रश्न
In the adjoining figure, O is the centre of the circle. From point R, seg RM and seg RN are tangent segments touching the circle at M and N. If (OR) = 10 cm and radius of the circle = 5 cm, then
- What is the length of each tangent segment?
- What is the measure of ∠MRO?
- What is the measure of ∠MRN?
Seg RM and seg RN are tangent segments of a circle with centre O. Prove that seg OR bisects ∠MRN as well as ∠MON with the help of activity.
In the given figure, seg EF is a diameter and seg DF is a tangent segment. The radius of the circle is r. Prove that, DE × GE = 4r2
Four alternative answers for the following question is given. Choose the correct alternative.
Length of a tangent segment drawn from a point which is at a distance 12.5 cm from the centre of a circle is 12 cm, find the diameter of the circle.
In the given figure, M is the centre of the circle and seg KL is a tangent segment.
If MK = 12, KL = \[6\sqrt{3}\] then find –
(1) Radius of the circle.
(2) Measures of ∠K and ∠M.
In the following figure ‘O’ is the centre of the circle.
∠AOB = 1100, m(arc AC) = 450.
Use the information and fill in the boxes with proper numbers.
(i) m(arcAXB) =
(ii)m(arcCAB) =
(iv)∠COB =
(iv)m(arcAYB) =
The perpendicular height of a cone is 12 cm and its slant height is 13 cm. Find the radius of the base of the cone.
In the given figure, M is the centre of the circle and seg KL is a tangent segment. L is a point of contact. If MK = 12, KL = `6sqrt3`, then find the radius of the circle.
Segment DP and segment DQ are tangent segments to the circle with center A. If DP = 7 cm. So find the length of the segment DQ.
Length of a tangent segment drawn from a point which is at a distance 15 cm from the centre of a circle is 12 cm, find the diameter of the circle?
In the adjoining figure, O is the center of the circle. From point R, seg RM and seg RN are tangent segments touching the circle at M and N. If (OR) = 10 cm and radius of the circle = 5 cm, then
(i) What is the length of each tangent segment?
(ii) What is the measure of ∠MRO?
(iii) What is the measure of ∠MRN?
In the adjoining figure circle with Centre, Q touches the sides of ∠MPN at M and N. If ∠MPN = 40°, find measure of ∠MQN.
The figure ΔABC is an isosceles triangle with a perimeter of 44 cm. The sides AB and BC are congruent and the length of the base AC is 12 cm. If a circle touches all three sides as shown in the figure, then find the length of the tangent segment drawn to the circle from point B.
In a parallelogram ABCD, ∠B = 105°. Determine the measure of ∠A and ∠D.
In the following figure, XY = 10 cm and LT = 4 cm. Find the length of XT.
A circle touches side BC at point P of the ΔABC, from outside of the triangle. Further extended lines AC and AB are tangents to the circle at N and M respectively. Prove that : AM = `1/2` (Perimeter of ΔABC)
