# Selina Solutions Class 9 Mathematics Solutions for Exercise 9(A) in Chapter 9 - Chapter 9- Triangles [Congruency in Triangles]

Question 3 Exercise 9(A)

The following figure shows a circle with center O.

Solution

Video transcript
"hello students my name is rabbit singh and i welcome you all to leader learning homework one of india's best online classes now today in this video we have a question that is based on the topic of circle the question says the following figure shows a circle with center o the circle is given and center o is given and sides are given a b points on the circle and o to b we have drawn a perpendicular so if op is perpendicular to a b then prove that ap is equal to p b that means this side will be equal to this side now first of all let us draw the construction part let us draw oa and ob this is the external construction that we are doing now we will start the proof now you can check in triangles oap that means o ap and triangle o b p o a is equal to ob why because they are radius this and this are radii this is also equal to radius so that's why they are equal now side op you can check this perpendicular this is common so that would be common now based on right angle this is right angle so based on right angle hypotenuse side criteria of congruency triangle o ap is congruent to triangle obp that we have proved now what we have to prove but ap is equal to bp so if you check these two triangles are congruent so that means ap will be equal to bp because y c b c d corresponding parts of congruent triangles so based on that p becomes a midpoint of a b so hence proof so i hope you have understood the concept very clearly but still if you have any doubt do comment in the comment box and please like and subscribe our channel for lido thank you"
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