A geometry problem by Mehul Chaturvedi

Geometry Level 3

A circle with centre $O$ is touching two intersecting lines $AX$ and $BY$ . The two points of contact $A$ and $B$ subtend an angle of 65 degreess at any point C on the circumference of the circle. If $P$ is the point of the intersection of the two lines, then find the measure of angle $APO$ given that straight lines $AP$ and $PB$ are tangents.

The answer is 25.

2 solutions

Vasudev Chandna
Apr 6, 2015

Angle AOB= 2xAngle ACB= 130

Now, Angle AOP= Half Angle ACB= 65

By angle sum property, we get Angle APO= 180- (65+90)

= 180- 155

=25

Piyush Maheshwari
Oct 23, 2014

We know, Angle AOB = 2 angle ACB = 130 NOW In AOBP- angle APB= 360-(90+90+130)=50 Also, ∆APO =~ ∆BPO Thus angleAPO = angle BPO = 25

@Mehul Chaturvedi This problem has been flagged as it is unclear if AP and PB are tangents. That seems to be an assumption in the solution, but it is not stated in the problem. The diagram also seems to suggest that AP is not a tangent, as it cuts the circle again.

Calvin Lin Staff - 6 years, 7 months ago

Now,..Is that correct Mr. @Calvin Lin

Mehul Chaturvedi - 6 years, 7 months ago

A geometry problem by Mehul Chaturvedi

The answer is 25.

2 solutions

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