10

Circles

10th Class - CBSE - Mathematics - 1123 Questions - 0 Concepts

Important Questions

Q1 Subjective Hard
In the given figure, a circle touches all the four side of quadrilateral ABCD with AB=6 cm, BC=7 cm and CD=4 cm. Find AD.

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Q2 Subjective Hard
If $$\triangle ABC$$ is isosceles with $$AB =AC$$ and $$C (0, r)$$ is the incircle of the $$\triangle ABC$$ touching $$BC$$ at $$L$$, prove that $$L$$ bisect $$BC$$ ?

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Q3 Single Correct Hard
P and Q are two points on a circle with centre at O. R is a point on the minor arc of the circle between the points P and Q. he tangents to the circle at the pints p and Q meet each other at the point S. If $$\angle PSQ=\ 20,\ \angle PRQ=?$$
  • A. 80
  • B. 200
  • C. 160
  • D. 100

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Q4 Multiple Correct Hard
If a ray light passing through (-3,1) reflects on x-axis at A and the reflected ray is tangential to the circle $${ x }^{ 2 }+{ y }^{ 2 }=1$$ at p, then
  • A. The reflected ray is $$4x-3y+5=0$$
  • B. The reflected ray is $$3x-4y+5=0$$
  • C. Area of $$\Delta APO=\dfrac { 2 }{ 3 } $$sq. units('O' is origin)
  • D. Point P is $$\left( -\dfrac { 3 }{ 5 } ,\dfrac { 4 }{ 5 } \right) $$

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Q5 Subjective Hard
Two tangents PT and PT' are drawn to a circle, with centre O, from an external point P. Prove that $$\angle$$TPT'$$=2\angle$$OTT'.

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Q6 Single Correct Hard
Triangle PAB is formed by three tangents to circle O and $$measuredangle APB = 40^0$$; then angle AOB equals:
  • A. $$45^0$$
  • B. $$50^0$$
  • C. $$55^0$$
  • D. $$60^0$$
  • E. $$70^0$$

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Q7 Subjective Hard
Two tangents 12 cm long are drawn to a circle from the same point, and the distance between the points of tangency is 14.4 cm. Find the radius of the circle.

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Q8 Matrix Hard
If two tangents PA and PB are drawn to a circle with centre O from an external point P (figure), then match the column.
$$\angle PAB$$ $$90^0$$
$$\angle OAP$$ $$\theta /2$$
$$\angle OAB$$ $$90-\frac {\theta}{2}$$
$$\angle AOB$$ $$180^0-\theta$$

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Q9 Subjective Hard
Find the equation of the circle passing through three points(4, 7), (5, 6), and (1, 8). Also, find the coordinates of the point of intersection of the tangents to the circle at the points where it is cut by the straight line 5x+ y + 17 = 0.

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Q10 Subjective Hard
If $$O$$ is the centre of a circle, $$PQ$$ is a chord and the tangent $$PR$$ at $$P$$ makes an angle of $$50^0$$ with $$PQ$$ , then find the Angle$$(POQ)$$.

Asked in: Mathematics - Circles


1 Verified Answer | Published on 07th 09, 2020

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Questions 122475
Subjects 10
Chapters 93
Enrolled Students 65
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