geometry: triangle ABC is right-angled at B; circle so that  TOPIC_SOLVED

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geometry: triangle ABC is right-angled at B; circle so that

Postby marty.frmn on Tue Nov 03, 2009 9:48 pm

a triangle ABC is right-angled at B.... a circle is drawn such that it cuts AB at points P and Q such that BP=6cm and BQ=9.75cm. The side BC is tangent to this circle. Got to find the radius of this circle....
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Postby stapel_eliz on Tue Nov 03, 2009 10:02 pm

What is the length of PQ?

Draw the altitude line from the center of the circle down to side AB, bisecting PQ at a right angle. What is the length from the bisection point to P?

Draw the radius line from the center of the circle to side BC. Label this as "r". Note that, by nature of tangency, this radius must be perpendicular to BC.

Using BP and the length found above, what is the distance from B to the bisection point?

How does this relate to the radius? :wink:
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