Embibe Experts Solutions for Chapter: Polygon, Exercise 1: IOQM - PRMO and RMO 2019 (25-08-2019)

Author:Embibe Experts

Embibe Experts Mathematics Solutions for Exercise - Embibe Experts Solutions for Chapter: Polygon, Exercise 1: IOQM - PRMO and RMO 2019 (25-08-2019)

Attempt the free practice questions on Chapter 13: Polygon, Exercise 1: IOQM - PRMO and RMO 2019 (25-08-2019) with hints and solutions to strengthen your understanding. EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS solutions are prepared by Experienced Embibe Experts.

Questions from Embibe Experts Solutions for Chapter: Polygon, Exercise 1: IOQM - PRMO and RMO 2019 (25-08-2019) with Hints & Solutions

MEDIUM
IOQM - PRMO and RMO
IMPORTANT

Let ABCD be a square with side length 100.  A circle with centre C and radius CD is drawn. Another circle of radius r, lying inside ABCD, is drawn to touch this circle externally and such that the circle also touches AB and AD. If r=m+nk. Where m, n are integers and k is a prime number, find the value of m+nk.

EASY
IOQM - PRMO and RMO
IMPORTANT

Two sides of a regular polygon with n sides, when extended, meet at an angle of 28°. What is the smallest possible value of n?

HARD
IOQM - PRMO and RMO
IMPORTANT

From a square with sides of length 5, triangular pieces from the four corners are removed to form a regular octagon. Find the area removed to the nearest integer?

HARD
IOQM - PRMO and RMO
IMPORTANT

Let t be the area of a regular pentagon with each side equal to 1. Let P(x)=0 be the polynomial equation with least degree, having integer coefficients, satisfied by x=t and the gcd of all the coefficients equal to 1 . If M is the sum of the absolute values of the coefficients of P(x). What is the integer closest to M? sin18°=5-14

HARD
IOQM - PRMO and RMO
IMPORTANT

A point P in the interior of a regular hexagon is at distance 8,8,16 units from three consecutive vertices of the hexagon, respectively. If r is radius of the circumscribed circle of the hexagon, what is the integer closest to r?