Question

HLO GUYS , give me please my question answer ...​

Answer 1

Question :- In a circle (O,r) BC is a chord and P is a point on major arc BC as shown in figure. Prove that angle x + angle y = 90°

Solution :-

Given :- A circle with Centre O, BC is a chord and P is point on major arc BC.

To prove :- x + y = 90°

Construction :- Join OB.

Now, OB = OC (radius of circle)

So, ∆OBC is isoceles triangle. Hence, angle OBC = angle OCB

Give that angle OCB = y

hence, angle OBC = y

Now, we know that :-

"Angle subtended by a chord at any point on circumference of circle is half of the angle subtended by it at the centre"

Hence, angle BOC = 2 × angle BPC

Given angle BPC = x

So, angle BOC = 2x

Now, in ∆OBC, by applying angle sum property we get

angle OBC + Angle OCB + angle BOC = 180°

→ y + y + 2x = 180°

→ 2y + 2x = 180°

Take 2 as common,

→ 2(x + y) = 180°

→ (x + y) = 180/2

→ (x + y) = 90°

angle x + angle y = 90°

Hence proved