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.

1 Verified Answer | Published on 07th 09, 2020

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 $BC$ ?

1 Verified Answer | Published on 07th 09, 2020

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

1 Verified Answer | Published on 07th 09, 2020

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 $\left( -\dfrac { 3 }{ 5 } ,\dfrac { 4 }{ 5 } \right)$

1 Verified Answer | Published on 07th 09, 2020

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'.

1 Verified Answer | Published on 07th 09, 2020

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. $70^0$

1 Verified Answer | Published on 07th 09, 2020

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.

1 Verified Answer | Published on 07th 09, 2020

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.
 $\angle PAB$ $90^0$ $\angle OAP$ $\theta /2$ $\angle OAB$ $90-\frac {\theta}{2}$ $\angle AOB$ $180^0-\theta$

1 Verified Answer | Published on 07th 09, 2020

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.

1 Verified Answer | Published on 07th 09, 2020

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$(POQ)$.