Question 1 :
Does a diameter AB of a circle bisects all those chords which are parallel to the tangent at the point A?
Question 2 :
To divide a line segment AB in the ratio 4:7, a ray AX is drawn first such that ∠BAX is an acute angle and then points $A_1,A_2,A_3,.........$ are located at equal distances on the ray AX and the point B is joined to
Question 3 :
Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts.
Question 4 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b55273b23058497997f.PNG' />
In the above figure, The tangent at a point C of a circle and a diameter AB when extended intersect at P. If $\angle PCA=110^{\circ}$ , what is the value of $\angle CBA$?
Question 5 :
Draw an equilateral triangle ABC of each side 4 cm. Construct a triangle similar to it and of scale factor $\frac{3}{5}$ . Is the new triangle also an equilateral?
Question 6 :
From an external point P, two tangents, PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn which intersects PA and PB at C and D, respectively. If PA = 10 cm, what is the perimeter of the triangle PCD?
Question 7 :
Can we construct as many concentric circles as we want to a given circle?
Question 8 :
To construct a triangle similar to a given ∆ABC with its sides $\frac{8}{5}$ of the corresponding sides of ∆ABC draw a ray BX such that ∠CBX is an acute angle and X is on the opposite side of A with respect to BC. The minimum number of points to be located at equal distances on ray BX is
Question 9 :
To divide a line segment AB in the ratio p : q (p, q are positive integers), draw a ray AX so that ∠BAX is an acute angle and then mark points on ray AX at equal distances such that the minimum number of these points is equal to?
Question 10 :
Let s denote the semi-perimeter of a triangle ABC in which BC = a, CA = b, AB = c. If a circle touches the sides BC, CA, AB at D, E, F, respectively, Is it TRUE or FALSE that BD = s – b?
Question 11 :
To divide a line segment AB in the ratio 5:7, first a ray AX is drawn so that ∠BAX is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is
Question 12 :
State true or false. Construction of the pair of tangents from an external point to a circle is possible..
Question 13 :
Two circles with centres O and $O ^ { \prime }$ of radii 3 cm and 4 cm, respectively intersect at two points P and Q such that OP and $O ^ { \prime }P$ are tangents to the two circles. What is the length of the common chord PQ?
Question 14 :
Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8 cm is a tangent to the inner circle. What is the radius of the inner circle?
Question 15 :
Do the centre of a circle touching two intersecting lines lies on the angle bisector of the lines?
Question 16 :
Draw a circle of radius 4 cm. Construct a pair of tangents to it, the angle between which is 60$^{\circ}$. Also justify the construction. Measure the distance between the centre of the circle and the point of intersection of tangents.
Question 17 :
Do the tangents drawn at the ends of a chord of a circle make equal angles with the chord?
Question 18 :
Two tangents PQ and PR are drawn from an external point to a circle with centre O. Is QORP is a cyclic quadrilateral?
Question 19 :
To draw a pair of tangents to a circle which are inclined to each other at an angle of 35$^{\circ}$, it is required to draw tangents at the end points of those two radii of the circle, the angle between which is ( in degrees)?
Question 20 :
State True / False, by geometrical construction, it is possible to divide a line segment in the ratio $\begin{array}{l}2+\sqrt{3}:2-\sqrt{3}\end{array}$.
Question 21 :
A chord PQ of a circle is parallel to the tangent drawn at a point R of the circle. Does R bisects the arc PRQ?
Question 22 :
A is a point at a distance 13 cm from the centre O of a circle of radius 5 cm. AP and AQ are the tangents to the circle at P and Q. If a tangent BC is drawn at a point R lying on the minor arc PQ to intersect AP at B and AQ at C, what is the perimeter of the $\triangle ABC$?
Question 23 :
Two line segments AB and AC include an angle of 60$^{\circ}$ where AB = 5 cm and AC = 7 cm. Locate points P and Q on AB and AC, respectively such that AP = $\frac{3}{4}$ AB and AQ = $\frac{1}{4}$ AC. Join P and Q and measure the length PQ.
Question 24 :
Can we construct a triangle similar to a given triangle as per the given scale factor ?
Question 25 :
Draw a parallelogram ABCD in which BC = 5 cm, AB = 3 cm and ∠ABC = 60$^{\circ}$, divide it into triangles BCD and ABD by the diagonal BD. Construct the triangle BD' C' similar to ∆BDC with scale factor $\frac{4}{3}$ . Draw the line segment D'A' parallel to DA where A' lies on extended side BA. Is A'BC'D' a parallelogram?
