Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle

If a square ABCD is inscribed in a circle and AB =$4 cm$., then the radius of circle is-

If the length of a chord of a circle at a distance of $4$cm from the centre is $6$cm, then the diameter of the circle is-

Let $∆\mathrm{ABC}$ be an equilateral triangle. Let $BE\perp CA$ meeting $CA$ at $E$, then find the value of $(A{B}^2 +B{C}^2 +C{A}^2)$.

One chord of a circle is known to be $10.1$$cm$. The radius of this circle must be:

In the given figure $O$ is the Centre of a circle $OM=3 cm and AB=8 cm$. Find the radius of the circle?

The lengths of three medians of a triangle are $9 \mathrm{cm}$, $12 \mathrm{cm}$ and $15 \mathrm{cm}$. The area (in $\mathrm{sq}. \mathrm{cm}.$) of the triangle is:

The triangle $△\mathrm{ABC}$ and $△\mathrm{DEF}$ are similar and the areas are respectively $81 {\mathrm{cm}}^2$ and $196 {\mathrm{cm}}^2$. If $EF = 19.6 \mathrm{cm}$ then find the length of the side $BC$.

The difference between the circumference and semi-diameter of a circle is $37 \mathrm{m}$. What is the diameter of the circle?

AB is the chord of a circle with centre O and DOC is a line segment originating from a point D on the circle and intersecting AB produced at C such that BC = OD. If angle BCD $= 20°$, then angle AOD = ?

If the points $A(4,3)$and $B(x,5)$are on the circle with Centre$O(2,3)$. Find the value of $x$.

If two concentric circles are of radii $5 cm \& 3 cm$, then the length of the chord of the larger circle which touches the smaller circle is-

Find the length of the common chord of two circles of radii $12cm$ and $16 cm$, where the distance between their centres is $20cm.$

In a right-angled $∆ABC$, right angle at $A$, if $AD\perp BC$ such that $AD=p$. If $BC=a$, $CA=b$ and $AB=c$, then which relation is true?

In a$\mathrm{\Delta ABC},$$\frac{\mathrm{AB}}{\mathrm{AC}}=\frac{\mathrm{BD}}{\mathrm{BC}},\angle \mathrm{B}=70°$ and $\angle \mathrm{C}=50°$, then $\angle \mathrm{BAD}=$ ______.

A polygon has $54$diagonals. The number of sides in the polygon is_______?

PQ and QR are two chords of a circle and they are equally inclined to the diameter drawn through. What is the relation between PQ and QR?

If A is the area of a right angled triangle and b is one of the sides containing the right angle, then what is the length of the altitude on the hypotenuse?

With vertices of a triangle $ABC$ as centres, three circles are drawn, each touching the other two externally. If the sides of the triangle are $9 \mathrm{cm}$, $7 \mathrm{cm}$ and $6 \mathrm{cm}$, then what will be the radii of the circles?

 If in $△\mathrm{ABC}$ and $∆\mathrm{DEF},\angle \mathrm{A}=50°,\angle \mathrm{B}=70°,\angle \mathrm{C}=60°,\angle \mathrm{D}=60°,\angle \mathrm{E}=70°$ and $\angle \mathrm{F}=50°$ . Which of the following is correct?

Two chords $AB$ and $CD$ of circle whose centre is $O$, meet at the point $\angle OAC=50°, \angle BOD=40°$P. Find the value of $\angle BPD$ is