Question

divide a line segment PQ in the ratio a : b (a, b are positive integers), draw a ray PX so that ∠QPX is an acute angle and then mark points on ray PX at equal distances such that minimum
8.
9. 10.
A circle is inscribed in a ∆ABC having sides AB = 10 cm, BC = 12 cm and CA = 16 cm and circle touches the sides AB, BC and AC of triangle ABC at P, Q and R respectively. Find AP, BQ and CR. [3]
Two circles of equal radius 6 cm such that the distance between their centres is 15 cm, find the length of transverse common tangent. [3]
In the given figure, two circles C1 and C2 touch
each other internally at Q with centres O and O′ respectively. If radii of bigger and smaller circles are 4 cm and 3 cm respectively and ACDB is the
straight line of 2 15 cm, then find the lengths of OA and AC. [4]
CA
2 CC1
P O′OQ D
B
Oisthecentreofacircleofradius6cm.Pisa point such that OP = 10 cm and OP intersects the circle at T and PC, PD are two tangents drawn to the circle. If AB is the tangent to the circle at T, find the length AB. [4]
CA
6 cm
number of these points is (1) Greaterofaandb (3) a+b–1
(2) a+b
[1]
(4) a+b+1

Answer 1

Given : divide a line segment PQ in the ratio a : b (a, b are positive integers), draw a ray PX so that ∠QPX is an acute angle and then mark points on ray PX at equal distances

To Find :  minimum number of these points is

(1) Greater ofa and b

(2) a+b

(3) a+b–1

(4) a+b+1

Solution:

To divide a line segment PQ  in the ratio a:b,

Step1 : Draw a line segment PQ  of some length

Step 2 :  Draw a Ray PX such that ∠QPX is an acute angle

Step 3:  Take a+b point on PX of Equal length one by one ( consecutively)

Step 4 :  Join a+b th Point with Q as a straight line

Step 5 : Draw a line parallel to line drawn in step 4 such that it passes through ath point of step 3 and intersect PQ at M

M divides PQ in to  a : b Ratio.

a+b points are required  

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