Two circles intersect at two points b and c

Asked by admin @ 12/08/2021 in Math viewed by 317 People

"Question 9 Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see the given figure). Prove that ∠ACP = ∠QCD.

Class 9 - Math - Circles Page 186"

Answered by admin @ 12/08/2021

Solution:

Given: Two circles intersect at two points B & C. Through B, two line segments ABD & PBQ are drawn which intersect the Circles at A, D, P & Q.

To Prove:

∠ACP = ∠QCD

Proof:

In circle I,

For chord AP,

∠PBA = ∠ACP (Angles in the same segment are equal) — (i)

In circle II,

For chord DQ,

∠DBQ = ∠QCD (Angles in same segment) — (ii)

ABD and PBQ are line segments intersecting at B.

∠PBA = ∠DBQ (Vertically opposite angles) —iii

From the equations (i), (ii) and (iii),

∠ACP = ∠QCD

=°===============
========================
Hope this will help you.....

Two circles intersect at two points b and c

Similar Questions

Two circles intersect at two points a and b

A line that intersects a circle in two points

A line which intersects a circle at two points

How to find a point of intersection with two equations

A tangent to a circle intersects it in points

If two equal chords of a circle intersect

A and b are two points 150 km apart

The point of intersection of two ogive curve is

The point of intersection of two ogive curves is

Which step should be used to prove that point a is equidistant from points c and b?

At what points will the line y = x intersect the unit circle x2 + y2 = 1?

Two point charges a and b having charges

Two diameters of a circle will necessarily intersect

How to find equation of a circle with two points

P is a point equidistant from two intersecting lines

Most viewed questions in Math

What is the value of x in the expression

Shubham is facing south and moves 30 km

Prachi excellence in mathematics class 7 solutions pdf free download

Oxford new enjoying mathematics class 7 solutions chapter 1

Survey of various types of bank accounts icse project

The town of p is located at point x

A clock gains 4 minutes after every 4 minutes

Running a tuck shop or canteen maths project pdf

Paul is sixteenth from the front of the row

The average weight of 20 teachers is 80 kg

The number 567 xy is completely divisible by 30

In a row of friends tiya occupies fifteenth place

What would $ mean if fat is coded as

Consider a 3 digit integer x with distinct digits

Rahul went to his mother's mother in law