Embibe Experts Solutions for Chapter: Advance Maths, Exercise 4: Exercise 4

PT is a tangent to a circle of radius $6 cm$. If P is at a distance of $10 cm$ from the centre O. PBC is recant line and PB = $5 cm$, then what is the length of the chord BC?

Two circles ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$  touch each other internally at P. Two lines PCA and PDB meet the circles ${\mathrm{C}}_1$ in C, D and ${\mathrm{C}}_2$ in A, B respectively. If $\angle \mathrm{BDC}={120}^{\circ }$, then the value of $\angle \mathrm{ABP}$ is _____

Number of sides of two regular polygons are in the ratio $1 : 2$ and each of their interior angles are in the ratio $2 : 3$. The number of sides of the polygons are ?

The ratio of an interior angle to the exterior angle of a regular polygon is $7:2$. The number of sides of the polygon is:

A polygon has $35$ diagonals. The number of sides of the polygon is-

In $∆ABC$, D and E are points on AB and AC respectively such that $DE\left|\right|BC$ and DE divides the $∆ABC$ into two parts of equal areas. Then ratio of AD and BD is ___

In the given figure, $ABCD$ is a cyclic quadrilateral and diagonals bisect each other at $P$. If $\angle DBC = 60°$ and $\angle BAC = 30°$, then $\angle BCD$is:

$AB$and $CD$ are chords of a circle intersecting at $P$ inside the circle. If , $AP = 18 \mathrm{cm}$, $CD = 18 \mathrm{cm}$ and $DP = 6 \mathrm{cm}$, then value of $BP$ is