If PQ is a tangent, then find the value of angle POQ + angle QPO
Answers
Answer:
∵ PQ is the tangent to the circle
ang PQO = 90° (the tangent at any part of the circle is ⊥r to the radius at
the pt of contact) ..........(1)
in Δle POQ
POQ + PQO + QPO =180° ( ASP of a Δle)
by (1)
POQ + QPO = 90°
hope it's useful...............
Step-by-step explanation:
If PQ is a tangent,then <POQ+ <QPO =90⁰
Step-by-step explanation:
we know that for a triangle sum of the interior angles is 180⁰
that is here,
<POQ+ <QPO +<OQP =180⁰
as the angle made by a tangent with line to centre of the circle is 90⁰
<OQP is 90⁰
then substitute value in a above equation we have
<POQ+ <QPO +90⁰ =180⁰
<POQ+ <QPO =180⁰-90⁰
<POQ+ <QPO =90⁰
thus the answer.
DEFINITIONS AND SOME IMPORTANT CONCEPTS TO KNOW
- Sum of the angles of the interior triangle of a triangle is 180⁰
- sum of the exterior angles of a triangle is 360⁰
- angle made by a tangent with radius (or diameter) of circle is 90⁰
- circle is set of points that are equidistant from a poin( centre of the circle).
- tangent is the line passing through only one point in a circle ,were it is perpendicular to the radius if the circle .
some more question to refer
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A regular pentagon ABCDE is fitted inside a regular hexagon APQRST such that P-B-Q, Q-C-R, R-D-S and S-E-T. Find m SED
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