Question
Construct a triangle ABC, such that AB= 6 cm, BC= 7.3 cm and CA= 5.2 cm. Locate a point which is equidistant from A, B and C.
✓
Answer
Steps of construction:
(i) Draw a line segment BC= 7.3 cm.
(ii) With Bas centre and radius 6 cm draw an arc.
(iii) With C as centre and radius 5.2 cm draw another arc which intersects the first arc at A.
(iv) Join AB and AC.
(v) Draw perpendicuIar bisector of BC , AB and AC.
In triangIe ABC, P is the point of intersection of AB , AC and BC.
Therefore, PA = PB, PB = PC, PC = PA.
Thus, circum-centre of a triangle is the point which is equidistant from all its vertices.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Given matrix $B=\left[\begin{array}{ll}1 & 1 \\ 8 & 3\end{array}\right]$ Find the matrix $X$ if, $X=B^2-4 B$. Hence, solve for $a$ and $b$ given $X\left[\begin{array}{l}a \\ b\end{array}\right]=\left[\begin{array}{c}5 \\ 50\end{array}\right]$
→A cylinderical container with diameter of base $42 \ cm$ contains sufficient water to submerge a rectangular soild of iron with dimesions $22\ cm \times 14 \ cm \times 10.5\ cm.$ find the rise in level of the water the solid is submerged.
→The area between the circumferences of two concentric circles is $2464 \ cm^2$. If the inner circle has circumference of $132 \ cm,$ calculate the radius of outer circle.
→Use factor theorem to factorise $6 x^3+17 x^2+4 x-12$ completely.
→Prove that $(5x - 4)$ is a factor of the polynomial $f(x) = 5x^3 - 4x^2 - 5x +4$. Hence factorize It completely.
→Using the remainder theorem, factorise completely the following polynomial: $3 x^3+2 x^2-19 x+6$
→Archana borrowed $Rs. 18,000$ from Ritu at $12\% \ p.a.$ compound interest. If at the end of the $1^{st}, 2^{nd},$ and $3^{rd}$ years, Archana returned $Rs. 5,250 , Rs. 5,875$ and $Rs. 6,875$ respectively, find the amount Archana has to pay Ritu at the end of the $4^{th}$ year to clear her debt.
→The following table gives the hights of plants in centimeter. If the mean height if plants is $60.95 \ cm$ ; find the value of $F$
→| Height $(cm)$ | $50$ | $55$ | $58$ | $60$ | $71$ | $70$ | $65$ |
| no of plants | $2$ | $4$ | $10$ | $f$ | $3$ | $4$ | $5$ |
Prove the following identity:
$
(\cot A-\operatorname{cosec} A)^2=\frac{1-\cos A}{1+\cos A}
$
→$
(\cot A-\operatorname{cosec} A)^2=\frac{1-\cos A}{1+\cos A}
$
In the given figure, O is the centre of the circumcircle ABC. Tangents at A and C intersect at P. Given angle AOB = 140° and angle APC = 80°; find the angle BAC.
